Question

If `alpha, beta` are the roots of `ax^(2) + bx + c = 0`, then find the quadratic equation whose roots are `alpha + beta, alpha beta`.
A. `ax^(2) + (ab-ac) x - c = 0`
B. `ax^(2) + (b-c) x - bc = 0`
C. `a^(2)x^(2) + (b-c) x - ac = 0`
D. `a^(2)x^(2) + (ab-ac) x - bc = 0`

Answer 1

Correct Answer - D
`alpha + beta` are the root of `ax^(2) + bx + c = 0`
`rArr alpha + beta = (-b)/(a)`
`alpha. Beta = (c )/(a)`
Quadratic equation whose roots are `alpha + beta`, and `alphabeta` is `x^(2)- ((-b)/(c) + (c )/(a)) x + (-b)/(a)xx c/a= 0`.
`x^(2) + ((b-c)/(a)) x - (bc)/(a^(2)) = 0`
`a^(2)x^(2) + (ab-ac) x - bc = 0`.