Advertisements
Advertisements
Questions
Find the zeroes of the quadratic polynomial f(x) = 5x2 – 4 – 8x and verify the relationship between the zeroes and coefficients of the given polynomial.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
5x2 – 4 – 8x
Advertisements
Solution
We have:
f(x) = 5x2 – 4 – 8x
= 5x2 – 8x – 4
= 5x2 – (10x – 2x) – 4
= 5x2 – 10x + 2x – 4
= 5x(x – 2) + 2(x – 2)
= (5x + 2) (x – 2)
∴ f(x) = 0 ⇒ (5x + 2) (x – 2) = 0
⇒ 5x + 2 = 0 or x – 2 = 0
⇒ `x = (-2)/5` or x = 2
So, the zeroes of f(x) are `(-2)/5` and 2.
Sum of zeroes =`((-2)/5) + 2`
= `(-2 + 10)/5`
= `8/5`
= `(-("Coefficient of" x))/(("Coefficient of" x^2))`
Product of zeroes = `((-2)/5) xx 2`
= `(-4)/5`
= `("Constant term")/(("Coefficient of" x^2))`
APPEARS IN
RELATED QUESTIONS
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in the following.
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
Find the zeros of the polynomial f(x) = x2 + 7x + 12 and verify the relation between its zeroes and coefficients.
Find the quotient and the remainder when f(x) = x3 – 3x2 + 5x – 3 is divided by g(x) = x2 – 2.
Find the zeros of the polynomial x2 – 3x – m(m + 3).
If one zero of the quadratic polynomial kx2 + 3x + k is 2, then find the value of k.
If 1 is a zero of the quadratic polynomial ax2 – 3(a – 1)x – 1 is 1, then find the value of a.
If –2 is a zero of the polynomial 3x2 + 4x + 2k, then find the value of k.
If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.
If 𝛼 and 𝛽 be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (𝛼 + 𝛽 + 𝛼𝛽).
Find the zeroes of the quadratic polynomial f(x) = 6x2 – 3.
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.
Consider the following statements.
- x – 2 is a factor of x3 – 3x² + 4x – 4.
- x + 1 is a factor of 2x3 + 4x + 6.
- x – 1 is a factor of x5 + x4 – x3 + x² -x + 1.
In these statements
If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.
The number of polynomials having zeroes – 3 and 4 is ______.
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
