The coefficient of x in the quadratic equation x2 + px + q = 0 was tak

1.	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 areA) 3 or -10 B) -3 or 10 C) -3 or -10 D) 3 or 10
Answer» 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. Correct option is C) -3 or -10

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 areA) 3 or -10 B) -3 or 10 C) -3 or -10 D) 3 or 10

Answer»

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.

Correct option is C) -3 or -10