Advertisements
Advertisements
Question
If ๐ผ and ๐ฝ are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
Advertisements
Solution
Since ๐ผ ๐๐๐ ๐ฝ are the roots of the quadratic polynomial
f(x) = ๐ฅ2 − 5๐ฅ + 4
Sum of roots = α + β = 5
Product of roots = αβ = 4
`1/alpha+1/beta-2alphabeta=(beta+alpha)/(alphabeta)-2alphabeta=5/4-2xx4=5/4-8=(-27)/4`
APPEARS IN
RELATED QUESTIONS
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
`p(x) = x^2 + 2sqrt2x + 6`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
Find a cubic polynomial whose zeroes are 2, -3and 4.
If ๐ผ, ๐ฝ are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.
The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
