Question

m, n are zeroes of $a{x}^2+7x+c$ Find the value of a and c if the sum of zeroes is -7 and sum of squares of zeroes is 25

• A. -1, 12
• B. -1, -12
• C. 1, 12
• D. 1, -12

Answer 1

The correct option is C 1, 12

The standard quadratic equation is $a{x}^2+bx+c=0$

Then Sum of roots = $-\frac{b}{a}$ and Product of roots = $\frac{c}{a}$

$m,n$ are zeroes of $a{x}^2+7x+c=0$

$m+n=-7$ [ Given ] ---- ( 1 )

$m^2+n^2=25$ [ Given ] ----- ( 2 )

$\Rightarrow$ $m+n=\frac{-7}{a}$

$\Rightarrow$ $-7=\frac{-7}{a}$ [ From ( 1 ) ]

$\therefore$ $a=1$

$\Rightarrow$ $(m+n{)}^2=m^2+n^2+2mn$

$\Rightarrow$ $(-7{)}^2=25+2mn$ [ From ( 1 ) and ( 2 ) ]

$\Rightarrow$ $49=25+2mn$

$\Rightarrow$ $24=mn$

$\Rightarrow$ $mn=12$ ----- ( 3 )

$\Rightarrow$ $mn=\frac{c}{a}$

$\Rightarrow$ $12=\frac{c}{1}$ [ From ( 3 ) ]

$\therefore$ $c=12$

$\therefore$ $a=1$ and $c=12$