When Are Roots Real and Equal?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.

How do you know if roots are real and equal?

To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c=0) , we need to caclulate the discriminant, which is b^2 – 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.

What does it mean when roots are equal?

A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots iff these roots are both equal to the root of the derivative.

When the roots of equation are equal?

The quadratic equation ax2 + bx + c = 0 has equal roots if its discriminant b2 – 4ac = 0.

What is the condition for real roots?

When a, b, c are real numbers, a 0: If = b² -4 a c = 0, then roots are equal (and real). If = b² -4 a c > 0, then roots are real and unequal. If = b² -4 a c < 0, then roots are complex.

What is real and equal?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.

What equation have real rational and equal roots?

When a, b and c are real numbers, a ≠ 0 and discriminant is zero (i.e., b2 – 4ac = 0), then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and equal.

What are real roots?

Given an equation in a single variable, a root is a value that can be substituted for the variable in order that the equation holds. In other words it is a “solution” of the equation. It is called a real root if it is also a real number. For example: x2−2=0.

Which of the quadratic equation has equal roots?

Answer: Using the standard ax^2 + bx + c =0, the quadratic will have two equal roots if the discriminant b^2 – 4ac = 0.

When roots are real and distinct?

If an equation has real roots, then the solutions or roots of the equation belongs to the set of real numbers. If the equation has distinct roots, then we say that all the solutions or roots of the equations are not equal. When a quadratic equation has a discriminant greater than 0, then it has real and distinct roots.

What is the nature of the roots of a quadratic equation if the discriminant is equal to zero?

Answer : If the value of the discriminant is 0, the roots of a quadratic equation are real and equal.

What is discriminant and nature of roots?

The sign of the discriminant tells us the nature of the solutions ( or roots ) of a quadratic equation. We can obtain two distinct real solutions if D>0, two non-real solutions if D<0 or one solution ( called a double root ) if D=0.

What does a discriminant of 0 mean?

A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

Which of the following has no real roots?

Solution: A quadratic equation ax2 + bx + c = 0 has no real roots if discriminant < 0.

Which of the following is equal to the product of the roots?

The product of the roots of a quadratic equation is equal to the constant term (the third term), divided by the leading coefficient.

When b2 4ac 0 and a perfect square the roots are?

(i) Roots are real and equal: If b2 -4ac = 0 or D = 0 then roots are real and equal. So the roots are equal which is 2. (ii) Roots are rational and unequal: If a,b,c are rational numbers and b2 -4ac is positive and perfect square then √b2−4ac b 2 − 4 a c is a rational number then the roots are rational and unequal.

What are two equal real roots?

The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots.

When roots are equal then discriminant?

If the roots of a quadratic equation are real & equal then the discriminant is zero.

What is the discriminant if the roots are equal?

If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots. D < 0 means no real roots.

What is the condition necessary for both of the roots of a quadratic to be real and negative?

CONDITIONS FOR BOTH ROOTS TO BE REAL & NEGATIVE: (1) If D > 0, there will be REAL roots. (2) If D>0, & all terms of the quadratic equation are positive then both roots will be NEGATIVE. (3) If D>0, & any one of the terms is negative.

What happens when the discriminant is less than zero?

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

Which condition satisfies if the roots of the quadratic equations are real *?

We also know that the roots of a quadratic equation are real if and only if the discriminant is non-negative, that is, if and only if b2−4c≥0. Using these facts, if α and β are both real and positive, then b=α+β>0, c=αβ>0 and b2≥4c, as above.


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