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**Short Answer Type Questions**

**Q.1. Find the quadratic polynomial, sum and product of whose zeroes are -1 and -20 respectively. Also, find the zeroes of the polynomial so obtained. **

**[CBSE 2019, (30/4/2)]****Ans:** Let α and β be the zeroes of the quadratic polynomial.

∴ Sum of zeroes, α + β = - 1

and Product of zeroes, α . β = - 20__Now, quadratic polynomial be:__= x

= x

= x

⇒ x = - 5,4

∴ zeroes are - 5 and 4

Equating p(x) = 0

⇒

⇒

Now, the sum of zeroes

and product of zeroes

Hence verified

f(x) = x

∴ Sum of zeroes =

⇒ α + β = 4

and product of zeroes,

= x

Let α and β be the zeroes of polynomial.

So,

∴

⇒

⇒ 2k + 12 = 4k - 2

⇒ 2k = 14 ⇒ k = 7

**[Delhi 2019]****Ans:** 1 is one of the zero of p(x) = 3x^{3} + 10x^{2} - 9x - 4

⇒ x = 1 satisfies the polynomial p(x)

∴ (x - 1) is a factor of p(x)

Hence (x - 1) divides p(x) completely.**Q.6. Find all zeroes of the polynomial (2x ^{4} - 9x^{3} + 5x^{2} + 3x - 1) if two of its zeroes are (2 + √3) and (2 - √3). [CBSE 2018]**

∵ α,β are zeroes of p(x)

∴ α + β = sum of zeroes = -b/a

Now a quadratic polynomial whose zeroes are 2α and 2β.

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 = α

∴ other zero = -α

Now Sum of zeroes =

⇒

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