Q). If the zeroes of the polynomial x² + p x + q are double in values to the zeros of 2 x² – 5 x – 3 Find the value of p and q.

Ans:

Step 1: Given polynomial equation 2 x² – 5 x – 3 = 0

Comparing with standard polynomial, ax² + b x + c = 0, we get,

a =  2, b = – 5, c = – 3

Step 2: Let’s consider that the roots of this polynomial be α and β.

and we know that sum of roots (α + β) = 

∴   α + β =   …………… (i)

Also, we know that the product of the roots (α x β) =

∴ α . β = …………. (ii)

Step 3: Given polynomial is:  x² + p x + q = 0 and its roots are double of earlier one i.e. 2 𝛼 and 2𝛽

Comparing with standard polynomial, ax² + b x + c = 0, we get,

a =  1, b = p, c = q

Step 4: ∵ Sum of roots = 

∴   2 α + 2 β = 

∴   p = 2 α + 2 β

=  2 (α + β)

= 2    [value taken from equation (i)]

∴   p = 5

Step 5: Also the product of the roots =

∴ 2 α . 2 β =

∴ 4 (α . β) = q

∴ q = 4        [value taken from equation (ii)]

∴ q = – 6

Therefore, the value of p and q are 5 and – 6 respectively.

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