Question

Write the condition for the roots to become equal in the equation ax? + bx + c = 0​

Answer 1

Answer:

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.

Answer 2

$\huge\boxed{\fcolorbox{red}{ink}{SOLUTION:}}$

The following condition are apply for the roots to become equal in the equation ax ²+ bx + c = 0

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• The value of discriminate should be 0 for equal equation

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• ⇒ The given quadratic equation is ax ²+bx+c=0

• Hence consider the root be
• α and β.

$⇒ α=−β \: \: \: \: \: [ Given ] \\⇒ α+β− a−b \\⇒ −β+β= a−−b \\⇒ 0= a −b \\∴ b=0 \: \: \: \: \: \: \: ( 1 )$

• We have one root negative so,

$∴ αβ<0 \\ \\∴ ac <0$

• Hence either c or a will be negative.

• It Means that a and c will be having opposite sign.

• a>0,c<0 or c>0,a<0 and b=0.

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$\huge\boxed{\dag\sf\red{Thanks}\dag}$