Question

The coefficient of x in the quadratic equation $a{x}^2+bx+c=0$ was wrongly taken as 17 in place of 13 and its roots were found to be –2 and –15, the actual roots of the equation are

• A. –2 and 15
• B. –3 and –10
• C. –4 and –9
• D. –5 and –6

Answer 1

The correct option is B

–3 and –10

New roots are – 2, – 15
$\therefore$ Quadratic equation is (x + 2) (x + 15) = 0
$\Rightarrow x^2+17x+30=0$
Correct quadratic is x² + 13x + 30 = 0
$\Rightarrow$ (x + 3) (x + 10) = 0
$\Rightarrow$ x = –10, – 3
Hence, actual roots are – 3, – 10.