Question

find the value of a and b for which x=3/4 and x=-2 are the roots of the equation ax2+bx-6=0

Answer 1

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Answer 2

Answer:

The value of a and b are 4 and 5 resp.

Step-by-step explanation:

$\text{Given that }x=\frac{3}{4}\text{ and x=-2 are the roots of the equation }ax^2+bx-6=0$

we have to find the value of a and b.

$\text{Roots are }x=\frac{3}{4}\text{ and x=-2}$

$\text{sum of roots=}\frac{3}{4}+(-2)=\frac{-5}{4}=\frac{-b}{a}$

$\text{Product of roots=}\frac{3}{4}\times (-2)=\frac{-3}{2}=\frac{-6}{a}$

$\frac{-3}{2}=\frac{-6}{a}$

$a=-6\times \frac{2}{-3}=4$

$\frac{-5}{4}=\frac{-b}{a}$

$b=\frac{5}{4}\times a=\frac{5}{4}\times 4=5$

The value of a and b are 4 and 5 resp.