Question

if à, b are the roots of the equation ax²+bx+c=0,then the value of 1/aa+b+1/ab+b​

Answer 1

Answer:

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Step-by-step explanation:

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