Ramesh and Mahesh solve a quadratic equation. Ramesh reads its constant term wrongly and finds its roots as $8$ and $2$ where as Mahesh reads the coefficient of $x$ wrongly and finds its roots as $- 11$ and $1$ . The correct roots of the equation are

11, 1

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- 11, 1

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11, - 1

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None of these

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Solution

The correct option is C $11, - 1$
According to Ramesh , roots were 2 and 8
$\Rightarrow (x - 8) (x - 2) = 0$
$\Rightarrow x^{2} - 10 x + 16 = 0$
Constant term 16 is wrong.
According to Ramesh , roots were -11, 1
$(x + 11) (x - 1) = 0$
$\Rightarrow x^{2} + 10 x - 11 = 0$
But 10 is wrong.
So, correct equation is
$x^{2} - 10 x - 11 = 0$
$(x - 11) (x + 1) = 0$
$x = 11, - 1$

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Ramesh and Mahesh solve a quadratic equation. Ramesh reads its constant term wrongly and finds its roots as 8 and 2 where as Mahesh reads the coefficient of x wrongly and finds its roots as −11 and 1. The correct roots of the equation are

The correct option is C 11,−1According to Ramesh , roots were 2 and 8⇒(x−8)(x−2)=0 ⇒x2−10x+16=0Constant term 16 is wrong.According to Ramesh , roots were -11, 1(x+11)(x−1)=0⇒x2+10x−11=0But 10 is wrong.So, correct equation isx2−10x−11=0(x−11)(x+1)=0x=11,−1

Ramesh and Mahesh solve a quadratic equation. Ramesh reads its constant term wrongly and finds its roots as $8$ and $2$ where as Mahesh reads the coefficient of $x$ wrongly and finds its roots as $- 11$ and $1$ . The correct roots of the equation are