Advertisements
Advertisements
Question
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Advertisements
Solution
We have,
`f(u)=5u^2+10u`
It can be written as 5u (u+2)
∴ `f(u)=0⇒ 5u=0or u+2=0`
⇒ `u=0 or u=-2 `
So, the zeroes of f (u) are −2 and 0.
Sum of the zeroes =`-2+0=-2=(-2xx5)/(1xx5)=-10/5 -(("Coefficient of x"))/(("Coefficient of" u^2))`
Product of zeroes=`-2xx0=0=(0xx5)/(1xx5)=-0/5= ("Constant term")/(("Coefficient of" u^2))`
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.
`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
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
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`.
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p.
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.
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
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).
The product of the zeros of x3 + 4x2 + x − 6 is
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
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`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
