Advertisements
Advertisements
प्रश्न
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
पर्याय
`7/3`
`(-7)/3`
`3/7`
`(-3)/7`
Advertisements
उत्तर
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to `underlinebb((-3)/7)`.
Explanation:
p(x) = 4x2 – 3x – 7 = 0
α, β are the roots of above equation
∴ α + β = `- ("Coefficient of" x)/("Coefficient of" x^2)`
= `-((-3))/4`
= `3/4`
and αβ = `"Constant term"/("Coefficient of" x^2)`
= `(-7)/4`
Now, `1/α + 1/β`
= `(β + α)/(αβ)`
= `(α + β)/(αβ)`
= `(3/4)/((-7)/4)`
= `(-3)/7`
संबंधित प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.
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 a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.
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.
Find a cubic polynomial whose zeroes are 2, -3and 4.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
Find a quadratic polynomial whose zeroes are 6 and – 3.
