The number of polynomials having zeroes as -2 and 5 is
a. 1
b. 2
c. 3
d. more than 3

Solution:

Given, the zeros of the polynomial are -2 and 5.

We have to find the number of polynomials that have zeros as - 2 and 5.

Here the polynomial is of the form

p(x) = ax² + bx + c

We know that

Sum of zeros = – (coefficient of x) ÷ coefficient of x² = -b/a

-2 + 5 = -b/a

3 = -b/a

b = -3 and a = 1

Product of the zeros = constant term ÷ coefficient of x² = c/a

c/a = (-2)(5)

c = -10

Now let us substitute a, b and c values in p (x)

x² - (3x) + (-10)

x² - 3x - 10

Therefore, the number of polynomials having zeros as -2 and 5 is more than 3.

Try this: The number of polynomials having zeroes as 3 and 5 is a. 1 b. 2 c. 3 d. more than 3

Given, the zeros of the polynomial are 3 and 5.

We have to find the number of polynomials that have zeros as 3 and 5.

Here the polynomial is of the form

p(x) = ax² + bx + c

We know that

Sum of zeros = – (coefficient of x) ÷ coefficient of x² = -b/a

-b/a = 3 + 5 = 8

b = 8 and a = 1

Product of the zeros = constant term ÷ coefficient of x² = c/a

c/a = (3)(5) = 15

c = 15

So, the quadratic polynomial can be written as

x² - (8x) + (15)

x² - 8x + 15

Therefore, the number of polynomials having zeros as 3 and 5 is more than 3.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 4

The number of polynomials having zeroes as -2 and 5 is a. 1, b. 2, c. 3, d. more than 3

Summary:

The number of polynomials having zeroes as -2 and 5 is more than 3

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