Advertisements
Advertisements
Questions
Find the zeroes of the quadratic polynomial f(x) = 6x2 – 3.
Write the zeros of the quadratic polynomial f(x) = 6x2 – 3.
Advertisements
Solution
To find the zeroes of the quadratic polynomial we will equate f(x) to 0
∴ f(x) = 0
⇒ 6x2 – 3 = 0
⇒ 3(2x2 – 1) = 0
⇒ 2x2 – 1 = 0
⇒ 2x2 = 1
⇒ `x^2 = 1/2`
⇒ `x = +- 1/sqrt(2)`
Hence, the zeroes of the quadratic polynomial f(x) = 6x2 – 3 are `1/sqrt(2), -1/sqrt(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).
Find the zeroes of the polynomial f(x) = x2 – 2x – 8 and verify the relation between its zeroes and coefficients.
One zero of the polynomial 3x3 + 16x2 + 15x – 18 is `2/3`. Find the other zeros of the polynomial.
Obtain all other zeroes of (x4 + 4x3 – 2x2 – 20x – 15) if two of its zeroes are `sqrt(5)` and `-sqrt(5)`.
If one zero of the polynomial x2 – 4x + 1 is `(2 + sqrt(3))`, write the other zero.
Find the zeros of the polynomial x2 – 3x – m(m + 3).
If 1 is a zero of the quadratic polynomial ax2 – 3(a – 1)x – 1 is 1, then find the value of a.
If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.
Find the zeroes of the quadratic polynomial `f(x) = 4sqrt(3)x^2 + 5x - 2sqrt(3)`.
If α, β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, find the value of k = ?
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.
The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.
A polynomial of degree n has ______.
The number of polynomials having zeroes as -2 and 5 is ______.
The number of polynomials having zeroes – 3 and 4 is ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
