Question

A quadratic polynomial, the sum of product of whose zeroes are 2 and -3/5 respectively is
a) 5x^2-3
b) 5x^2+3
c) 5x^2-10x+3
d) 5x^2-10x-3​

Answer 1

Answer:

Option (d)

5x² - 10x - 3

Note:

• If A and B are the zeros of a given quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

• If A and B are the zeros of a quadratic polynomial then it is given as ;

x² - (A+B)x + A•B.

Solution:

Given : Sum of zeros = 2

Product of zeros = -3/5

To find : A quadratic polynomial , the sum and product of which zeros are 2 and -3 respectively.

Let A and B are the zeros of the required quadratic polynomial , then ;

Sum of zeros = 2

=> A + B = 2

Also,

Product of zeros = -3/5

=> A•B = -3/5

Now,

The required quadratic polynomial will be given as ; x² - (A+B)x + A•B

=> x² - 2x + (-3/5)

=> x² - 2x - 3/5

=> (5x² - 10x - 3)/5

Also,

If A and B are zero of the polynomial ax² + bx + c then they are also the zeros of polynomial k(ax² + bx + c) .

Hence,

The required polynomial will be ;

5x² - 10x - 3 .