Question

If α,β are zeroes of polynomial p(x)= ax2+bx+c, find a quadratic Polynomial whose zeroes are 1/aα+b and 1/aβ+b​ plzzz anyone tell the answer ....

Answer 1

Answer:

Given α and β are the roots of the equation ax^2 + bx + c = 0. Therefore α+β = -b/a and αβ= c/a ………..(1)

Sum of the new roots = 1/a + α + 1/b + β = 1/a + 1/b -b/a = (a+b-b^2)/ab

Product of the new roots = ( 1/a + α )( 1/b + β ) = [(1+a α)/a](1+ bβ)/b] = [1+a(α+β)+αβ]/ab = [1+a(-b/a) + ab(c/a)]/ab = (1-b + bc)/ab

Hence the required quadratic equation is x^2- (sum of the roots) x + product of the roots = 0

i.e., x^2- [(a+b-b^2)/ab]x + (1-b + bc)/ab = 0

i.e., abx^2- (a+b-b^2)x + (1-b + bc)= 0

Answer 2

Answer:

Que : if a and b are the zeroes of the polynomial ax^2+bx+c then form the polynomial whose zeroes are 1/a and 1/b.