Question

The coefficient of x in the quadratic equation x² + px + q = 0 was taken as 17 in the place of 13 and its roots were found to be -2 and-15. The roots of the original equation are

A) 3 or -10 

B) -3 or 10 

C) -3 or -10 

D) 3 or 10

Answer 1

Correct option is (C) -3 or -10

When coefficient of x is 17 then -2 and -15 are roots of equation \(x^2+px + q = 0\)      _____________(1)

i.e., when p = 17, x = -2 is a root of equation (1)

\(\therefore(-2)^2+17\times-2+q=0\)

\(\Rightarrow4-34+q=0\)

\(\Rightarrow q=34-4=30\)

Now, let p = 13 then original quadratic equation becomes

\(x^2+13x+q=0\)

\(\Rightarrow x^2+13x+30=0\)    \((\because q=30)\)

\(\Rightarrow x^2+10x+3x+30=0\)

\(\Rightarrow x(x+10)+3(x+10)=0\)

\(\Rightarrow(x+10)(x+3)=0\)

\(\Rightarrow x+10=0\;or\;x+3=0\)

\(\Rightarrow x=-10\;or\;x=-3\)

Hence, -10 and -3 are roots of original equation.

Answer 2

Correct option is C) -3 or -10