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**Short Answer Type Questions**

**Q.1. Find the quadratic polynomial, sum and product of whose zeros are -1 and -20 respectively. Also, find the zeros of the polynomial so obtained. [CBSE 2019, (30/4/2)]****Ans:** Let Î± and Î² be the zeros of the quadratic polynomial.

âˆ´ Sum of zeros, Î± + Î² = - 1

and Product of zeros, Î± . Î² = - 20__Now, quadratic polynomial be:__= x

= x

= x

â‡’ x = - 5,4

âˆ´ zeros are - 5 and 4

Equating p(x) = 0

â‡’

â‡’

Now, sum of zeros

and product of zeros

Hence verified

f(x) = x

âˆ´ Sum of zeros =

â‡’ Î± + Î² = 4

and product of zeros,

= x

Let Î± and Î² be the zeroes of polynomial.

So,

âˆ´

â‡’

â‡’ 2k + 12 = 4k - 2

â‡’ 2k = 14 â‡’ k = 7

â‡’ x = 1 satisfies the polynomial p(x)

âˆ´ (x - 1) is a factor of p(x)

Hence (x - 1) divides p(x) completely.

âˆµ Î±,Î² are zeroes of p(x)

âˆ´ Î± + Î² = sum of zeroes = -b/a

Now a quadratic polynomial whose zeroes are 2Î± and 2Î².

x

**Long Answer Type Questions**

**Q.1. If one zero of the quadratic polynomial f(x) = 4x ^{2} - 8kx + 8x - 9 is negative of the other, then find zeroes of kx^{2} + 3kx + 2. [CBSE 2015]**

Let one zero = Î±

âˆ´ other zero = -Î±

Now Sum of zeroes =

â‡’

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