Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
उत्तर
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
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
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 a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
Find the quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
4x2 – 3x – 1
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
