Question

If b² - 4ac = O, then the nature of roots is
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Answer 1

Answer:

The nature of roots in quadratic equation is dependent on discriminant(b2 - 4ac). (i) Roots are real and equal: If b2 -4ac = 0 or D = 0 then roots are real and equal.

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.

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Answer 2

SOLUTION

TO FILL IN THE BLANK

If b² - 4ac = 0 , then the nature of roots is

EVALUATION

The general form of a quadratic equation is

ax² + bx + c = 0

We now apply the Sridhar Acharya formula

$\displaystyle \sf{ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }$

Since b² - 4ac = 0

Then we have

$\displaystyle \sf{ \implies x = \frac{ - b }{2a} }$

Hence the roots are real and equal

FINAL ANSWER

If b² - 4ac = 0 , then the nature of roots are real and equal

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