Question

One root of quadratic equation $8x^{2}+mx+15 = 0$ is $3\frac{x}{y} 4$. Find the value of m and the other root of the equation.

Answer 1

Given equation, 8x²+mx+15=0

One of the roots is 3/4, and hence it satisfies the given equation

So 8(3/4)²+m(3/4)+15=0

8(9/16)+m(3/4)+15=0

18/4+3m/4+15=0

Taking L.C.M, we have (18+3m+60)/4=0

18+3m+60=0

3m=−78

m=−26

Now, putting the value of m in the given equation, we get

8x²

+(−26)x+15=0

8x²−26x+15=0

8x²−20x−6x+15=0

4x(2x−5)−3(2x−5)=0

(4x−3)(2x−5)=0

So, 4x−3=0 or 2x−5=0

Therefore. x=3/4 or x=5/2