Advertisements
Advertisements
प्रश्न
The number of polynomials having zeroes as –2 and 5 is ______.
विकल्प
1
2
3
More than 3
उत्तर
The number of polynomials having zeroes as –2 and 5 is more than 3.
Explanation:
According to the question,
The zeroes of the polynomials = –2 and 5
We know that the polynomial is of the form,
p(x) = ax2 + bx + c.
Sum of the zeroes = – (Coefficient of x) ÷ Coefficient of x2 i.e.
Sum of the zeroes = – `b/a`
– 2 + 5 = `– b/a`
3 = `– b/a`
b = – 3 and a = 1
Product of the zeroes = Constant term ÷ Coefficient of x2 i.e.
Product of zeroes = `c/a`
(–2)5 = `c/a`
– 10 = c
Substituting the values of a, b and c in the polynomial p(x) = ax2 + bx + c.
We get, x2 – 3x – 10
Therefore, we can conclude that x can take any value.
APPEARS IN
संबंधित प्रश्न
Find a cubic polynomial whose zeroes are 2, -3and 4.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2x^2 + (7/2)x + 3/4`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
