Question

if alpha and beta are the
zeroes of Given p (x) = 4x^2 - x -4 find 1/alpha + 1/beta
(class 10th Maths chapter polynomial) ​

Answer 1

Simplify 1/alpha + 1/beta

Take lcm =alpha x beta

Now in numerator you will have alpha + beta

Now the simplified equation is alpha+beta/alpha x beta


Now we know relation between zeros and coefficient of polynomials, that in a quadratic equation ax^2+ bx+ c, whose zeros are alpha , and beta , alpha + beta = -b/a

And alpha x beta = c/a


Now according to your question, alpha + beta will be = 1/4

And alpha x beta =-1


So the answer to your question is alpha+beta / alpha x beta


= (1/4)/-1

Which is equal to -1/4

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