CMAT 2021 Solved Question Paper

Question : 6 of 100

Marks: +1, -0

Meera and Sarika attempted to solve a quadratic equation in

x

. Sarika made a mistake in reading the coefficient of

x

and obtained the roots as 12 and 16. Meera made a mistake in reading the constant term of the equation. She obtained the roots as 22 and 6. The corrects roots(s) is (are)
(A)

-16

(B)

-12

A and B
A and C
C and D
B and D

Validate

Solution:

We know the general form of a quadratic equation,

x^{2}- \text "(sum of roots) "x+ \text "(product of roots) "=0

∴ Equation of Sarika,

x^{2}-28 x+192=0

And equation of Meera,

x^{2}-28 x+132=0

∵ Sarika made the mistake in reading the co-efficient of

x

.
∴ The correct equation

x^{2}+28 x+192=0

⇒

x^{2}+16 x+12 x+192=0

⇒

x(x+16)+12(x+16)=0

⇒(x+16)(x+12)=0

∴

x=-12

x=-16

are the required roots.

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