the number of polynomials having zeros 2 and 1 is
options:
a) 1
b)2
c)3
d)more than 3
Answers
Answered by
23
Hi
ANSWER is d) more than 3
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The quadratic polynomial whose zeroes are m,n is k[x²-(m+n)x+mn], where k is a constant.
Here , m = 2 , n = 1 ,
polynomial should be k[x²-(2+1)x+2×1]
k[x²-3x+2] , we can put different values of k,
we can get infinitly many polynomials
Answered by
40
Answer:
Option(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 + 1 = -b/a
⇒ 3 = -b/a
⇒ 3/1 = -b/a
∴ b = -3 and a = 1.
(ii)
Product of zeroes = c/a
⇒ 2 * 1 = c/a
⇒ 2 = c/a
⇒ 2 = c
So, The equation is f(x) = x² - 3x + 2.
[We know that zeroes does not change if the polynomial is divided or multiplied by constant]
f(x) = kx² - 3kx + 2k {Where k is real number}
f(x) = (x²/k) - (3/k)x + (2/k) {k is a non-zero real number}
∴ Therefore, there are infinitely many polynomials i.e more than 3.
Hope it helps!
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