Q. 23.9( 364 Votes )

Find a quadratic

Answer :


(i)
, -1

we know that for a quadratic equation in the form ax2 + 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 4x2x − 4.


(ii)

we know that for a quadratic equation in the form ax2 + 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

and


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 ax2 + 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 ax2 + 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 ax2 + 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 ax2 + 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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