Advertisements
Advertisements
Question
If 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
Solution
By using the relationship between the zeroes of he quadratic polynomial. We have
Sum of zeroes=`(-("Coefficient of x"))/("Coefficient of "x^2)`Sum of zeroes = `"Constant term"/("Coefficient of" x^2) `
∴` ∝+β=-(-7)/5 and ∝β=1/5`
⇒` ∝+β =7/5 and ∝β=1/5`
Now,`1/∝+1/β= (∝+β)/(∝β)`
=`(7/5)/(1/5)`
= 7
APPEARS IN
RELATED QUESTIONS
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
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
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.
`(-8)/3, 4/3`
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
