Question

Find a quadratic polynomial, the sum, and product of whose zeroes are 7/3 and -2 respectively.

Answer 1

Answer:

Given that,

Sum of the zeroes = 7/3

.i. e., alpha + beta = 7/3

Product of zeroes = -2

i. e., alpha × beta = -2

Then the polynomial is of the form,

x² - (alpha + beta) × x + ( alpha × beta ) = 0

x² - 7/3 × x + (-2) = 0

x² - 7x/3 - 2 = 0

3x² - 7x - 6/3 = 0

3x² - 7x - 6

Then the polynomial is 3x² - 7x - 6

Answer 2

Answer:

Given = sum of roots = 7/3

Product of roots = -2

Let \alpha and \beta be the two zeroes of the quadratic polynomial.

We know that,

{x}^2- (sum of roots)x + (product of roots)

{x}^2 -7/3x + -2

Hence, {x}^2 -7/3x + -2 is the required quadratic equation