Question

If the sum of roots of 3x2-(3m-2)x-(m-6)=0 is equal to product of roots then find m

Answer 1

ax2+bx+c=0,

Sum of roots = −ba

Product of roots= ca

For the equation

3x2−(3k−2)x−(k−6)=0,

a=3,b=−(3k−2),c=−(k−6)

Sum of roots= −ba=−(−(3k−2))3=(3k−2)3

Product of roots = ca=−(k−6)3

From the given problem,

Sum of roots = Product of roots

⟹(3k−2)3=−(k−6)3

⟹3k−2=−k+6

⟹3k+k=6+2

⟹4k=8

⟹k=2