Advertisements
Advertisements
प्रश्न
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
Advertisements
उत्तर
Step 1: Use Sum and Product of Roots
Sum of roots: `alpha+beta = ("−coefficient of x")/("coefficient of" x^2)`
Product of roots: `alpha beta = ("constant term")/("coefficient of" x^2) = -2/1 = -2`
Step 2: Find `alpha/beta + beta/alpha`
`alpha/beta + beta/alpha = (alpha^2 + beta^2)/(alphabeta)`
α2 + β2 = (α + β)2 − 2αβ
Substituting known values:
α2 + β2 = (−1) 2 − 2(−2)
= 1 + 4 = 5
`alpha/beta + beta/alpha = 5/-2`
`= -5/2`
APPEARS IN
संबंधित प्रश्न
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 ˗ 10` and verify the relation between its zeroes and coefficients.
If 1is a zero of the quadratic polynomial `ax^2 – 3(a – 1)x – 1`is 1, then find the value of a.
If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find 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).
The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient 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 ______.
If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.
The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.
