Question

the number of polynomials having zeroes as -2 and 5 is_______
(a) 1
(b) 2
(c) 3
(d) more than 3

PLZ ANSWER WITH EXPLANATION!​

Answer 1

Answer:

D) more than 3

Step-by-step explanation:

Let the required Quadratic polynomial be f(x) = ax² + bx + c.

(i)

Sum of zeroes = -b/a

⇒ -2 + 5 = -b/a

⇒ 3 = -b/a

⇒ 3/1 = -b/a

∴ b = -3 and a = 1.

(ii)

Product of zeroes = c/a

⇒ -2 * 5 = c/a

⇒ -10 = c/a

⇒ c = -10

So, The equation is f(x) =  x² - 3x - 10

[We know that zeroes does not change if the polynomial is divided or multiplied by constant]

f(x) = kx² - 3kx - 10k  {Where k is real number}

f(x) = (x²/k) - (3/k)x - (10/k) {k is a non-zero real number}

∴ Therefore, there are infinitely many polynomials i.e more than 3.