Question

a quadratic polynomial whose zeroes are 1 and -3​

Answer 1

Step-by-step explanation:

Let the zeroes of the quadratic polynomial be

a = 1, ß = -3

Then, a + ß = 1+ (−3) = -2

aß = 1 × (-3) = −3

Sum of zeroes = a + ß = -2

Product of zeroes = aß = -3

Then, the quadratic polynomial = x² -

(sum of zeroes )x+ product of zeroes = x² (-2)x+ (-3) = x² + 2x - 3

Verification:

Sum of zeroes= a +B=1+(-3) = -2 or

(2) 1 = -2 Coefficient of x²

Coefficient of x

Product of zeroes = aß = (1)(-3) = -3 or -

Constant term

-3 1 Coefficient of x² = -3

So, the relationship between the zeroes and the coefficients is verified.