Question

Find a quadratic polynomial whose sum and
product of zeroes are - 7 and -8 respectively. [1]

Answer 1

Answer:

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Answer 2

Answer:

x² + 7x - 8

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros.

★ A quadratic polynomial can have atmost two zeros.

★ To find the zeros of the given polynomial , equate it to zero .

★ If A and B are the zeros of the quadratic polynomial p(x) = 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 any quadratic polynomial , then that quadratic polynomial is given by ; x² - (A+B)x + A•B .

Solution:

Here,

It is given that , the sum and product of zeros of the required quadratic polynomial are (-7) and (-8) respectively.

Now,

Sum of zeros of required quadratic polynomial will be given as ;

A + B = -7

Also,

The product of zeros of the required quadratic polynomial will be given as ;

A•B = -8

Thus,

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

ie ; x² - (-7)x + (-8)

ie ; x² + 7x - 8

Hence,

x² + 7x - 8 is the required quadratic polynomial.