Advertisements
Advertisements
Question
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
Advertisements
Solution
Since 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomials
p(y) = 5y2 – 7y + 1
Sum of the zeroes `alpha+beta="-coeeficient of x"/("coefficient of "x^2)`
`=-(-7)/5`
`=7/5`
Product of zeroes `=alphabeta="constant term"/"coefficient of "x^2`
`=1/5`
We have, `1/alpha+1/beta=(alpha+beta)/(alphabeta)`
By substituting `alpha+beta=7/5` and `alphabeta=1/5` we get,
`1/alpha+1/beta=(7/5)/(1/5)`
`1/alpha+1/beta=7/5xx5/1`
`1/alpha+1/beta=7`
Hence, the value of `1/alpha+1/beta` is 7
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`
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.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-3)/(2sqrt(5)), -1/2`
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
Find the zeroes of the polynomial x2 + 4x – 12.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
