Q. 24.0( 259 Votes )

# Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Answer :

(i) , -1

^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

Let a = 4, then b = -1, c = -4

Therefore, the quadratic polynomial is 4*x*^{2} − *x* − 4.

(ii)

we know that for a quadratic equation in the form ax^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

If a = 3, then b = , and c = 1

Therefore, the quadratic polynomial is

(iii) 0,

we know that for a quadratic equation in the form ax^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

If a = 1, then b = 0, c =

Therefore, the quadratic polynomial is .

(iv) 1, 1

we know that for a quadratic equation in the form ax^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

If a = 1, then b = -1, c = 1

Therefore, the quadratic polynomial is .

(v)

we know that for a quadratic equation in the form ax^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

If a = 4, then b = 1, c = 1

Therefore, the quadratic polynomial is .

(vi) 4, 1

we know that for a quadratic equation in the form ax^{2}+ bx + c = 0, and its zerors are α and β, then

sum of zeroes is

and product of zeroes is

Let the polynomial be , then

If a = 1, then b = -4, c = 1

Therefore, the quadratic polynomial is .

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PREVIOUSFind the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x2 - 2x - 8
(ii) 4s2 - 4s + 1
(iii) 6x2 - 3 - 7x
(iv) 4u2 + 8u
(v) t2 - 15
(vi) 3x2 - x - 4NEXTDivide the polynomial by the polynomial and find the quotient and remainder in each of the following :
(i)
(ii)
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