Similarly, we can take 'a' to be any real number. Let us say it is k. This gives -b/k = -3

or b = 3k and c/k = 2 or c = 2k. Substituting the values of a, b and c, we get the polynomial is kx2 + 3kx + 2k.

Example-6. Find the quadratic polynomial whose zeroes are 2 and -1/3, .


Solution : Let the quadratic polynomial be

ax2 + bx + c, a ≠ ø and its zeroes be α and β.

Here α = 2, β = -1/3,

Sum of the zeroes = (α + β) = 2 + [- 1/3]= 5/3

Product of the zeroes = (αβ) = 2 [-1/3] = 2/3

Therefore the quadratic polynomial ax2 + bx + c is

k[x 2 – (α + β)x + αβ], where k is a constant and k ≠ 0

i.e. k[x2 – 5/ 3 x – 2/ 3 ]

We can take different values for k.

When k = 3, the quadratic polynomial will be 3x2– 5x – 2.

Try This

i) Find a quadratic polynomial with zeroes -2 and 1/3

(ii) What is the quadratic polynomial the sum of whose zeroes is -3/2 and the product of the zeroes is -1.




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