Advertisements
Advertisements
рдкреНрд░рд╢реНрди
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 = ?
Advertisements
рдЙрддреНрддрд░
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes=`(-("Coefficent of x"))/("Cofficient of x"^2)` and Product of zeroes =`("Constant term")/("Coefficent of "x^2)`
`∴ ∝+β=-(-5)/1` and ∝β=k/1`
Solving ЁЭЫ╝ - ЁЭЫ╜ = 1 and ЁЭЫ╝ + ЁЭЫ╜ = 5, we will get
∝=3 and ЁЭЫ╜=2
Substituting these values in ЁЭЫ╝ЁЭЫ╜ =`k/1` we will get
`k = 6`
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).
Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ╦Ч 4 ╦Ч 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.
One zero of the polynomial `3x^3+16x^2 +15x-18 is 2/3` . Find the other zeros of the polynomial.
If f(x) =`x^3-3x+5x-3` is divided by g(x)=`x^2-2`
Find all the zeroes of polynomial `(2x^4 – 11x^3 + 7x^2 + 13x – 7)`, it being given that two of its zeroes are `(3 + sqrt2) and (3 – sqrt2)`.
If 3 is a zero of the polynomial `2x^2 + x + k`, find the value of k.
Write the zeros of the polynomial `f(x) = x^2 – x – 6`.
Find the zeroes of the quadratic polynomial `f(x) = 6x^2 – 3.`
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.
If one of the zeroes of the quadratic polynomial (k – 1) x2 + kx + 1 is - 3, then the value of k is ______.
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
A quadratic polynomial, whose zeores are -4 and -5, is ______.
If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is ______.
The number of polynomials having zeroes as -2 and 5 is ______.
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) 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 graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.
The given linear polynomial y = f(x) has
