Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If ЁЭЫ╝ and ЁЭЫ╜ be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (ЁЭЫ╝ + ЁЭЫ╜ + ЁЭЫ╝ЁЭЫ╜).
Advertisements
рдЙрддреНрддрд░
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes = `(-("Coefficient of x"))/("Coefficient of "x^2)`
Product of zeroes =`("Constant term")/("Coefficient of "x^2)`
a = 2, b = −7, and c = k
∴ ∝+ β = `(-b)/c`
= `(-(-7))/2`
= `7/2`
∝β = `c/a`
= `k/2`
Now, ЁЭЫ╝ + ЁЭЫ╜ + ЁЭЫ╝ЁЭЫ╜ = `7/2 + k/2`
= `(7 + k)/2`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
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 quadratic polynomial `f(x) = x^2 + 3x ╦Ч 10` and verify the relation between its zeroes and coefficients.
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero.
Find the zeroes of the polynomial `x^2 + x – p(p + 1) `
If 3 is a zero of the polynomial `2x^2 + x + k`, find the value of k.
If one zero of the quadratic polynomial `kx^2 + 3x + k is 2`, then find the value of k.
If the sum of the zeros of the quadratic polynomial `kx^2-3x + 5` is 1 write the value of k..
Find the zeroes of the quadratic polynomial `f(x) = 6x^2 – 3.`
If ЁЭЫ╝, ЁЭЫ╜ are the zeroes of the polynomial `f(x) = x^2 – 5x + k` such that ЁЭЫ╝ - ЁЭЫ╜ = 1, find the value of k = ?
Find the value of k such that the polynomial x2-(k +6)x+ 2(2k - 1) has some of its zeros equal to half of their product.
Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.
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 a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
If one of the zeroes of the quadratic polynomial (k -1)x² + kx + 1 the value of k is ______.
A polynomial of degree n has ______.
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
Which of the following is not the graph of a quadratic polynomial?
The number of polynomials having zeroes – 3 and 4 is ______.
