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 = ?
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╢реНтАНрди
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.
Find all the zeroes of `(2x^4 – 3x^3 – 5x2 + 9x – 3)`, it is being given that two of its zeroes are `sqrt3 and –sqrt3`.
Find the zeroes of the quadratic polynomial `f(x) = 6x^2 – 3.`
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then 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 x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.
If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is ______.
If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.
If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
