Question

if a and b are the zeros of the polynomial P of x is equal to 2 x square - 12 x + 2 y find the value of a2+b2​

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Maths

Polynomials

Relationship between Zeroes and Coefficients of a Polynomial

If a and b are the zeros of...

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Asked on December 20, 2019 by

Arpan Tangallapalli

If a and b are the zeros of the polynomial f(x)=x

2

−5x+k such that a-b = 1,find the value of k.

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ANSWER

Since a and b are the zeros of the polynomial f(x)=x

2

−5x+k

The standard quadratic equation is px

2

+qx+r=0

Then Sum of roots = −

p

q

and Product of roots =

p

r

Therefore,

a+b=5 and ab=k

Now, a−b=1

(a−b)

2

=1

(a+b)

2

−4ab=1

25−4k=1

24=4k

k=6