Question

If x = 1/2  and x = -3 are roots of the quadratic equation ax^2 + 7x + b = 0, find the values of a and b.

Answer 1

Answer:-

$\sf{The \ values \ of \ a \ and \ b \ are}$

$\sf{\frac{14}{5} \ and \ \frac{-21}{5} \ respectively. }$

Given:

• $\sf{Roots \ of \ the \ equation \ are \ \frac{1}{2} \ and \ -3}$

• $\sf{The \ given \ quadratic \ equation \ is}$
• $\sf{ax^{2}+7x+b=0}$

To find:

• The value of a and b.

Solution:

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{ax^{2}+7x+b=0}$

$\sf{Here, \ a=a, \ b=7 \ and \ c=b}$

$\sf{\frac{-b}{a}=\frac{1}{2}+(-3)}$

$\sf{\therefore{\frac{-7}{a}=\frac{1-6}{2}}}$

$\sf{\therefore{\frac{-7}{a}=\frac{-5}{2}}}$

$\sf{\therefore{a=\frac{14}{5}}}$

$\sf{\frac{c}{a}=\frac{1}{2}\times(-3)}$

$\sf{\therefore{\frac{b}{a}=\frac{-3}{2}}}$

$\sf{\therefore{b=\frac{-3}{2}\times\frac{14}{5}}}$

$\sf{\therefore{b=\frac{-21}{5}}}$

$\sf\purple{\tt{\therefore{The \ values \ of \ a \ and \ b \ are}}}$

$\sf\purple{\tt{\frac{14}{5} \ and \ \frac{-21}{5} \ respectively. }}$