Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Advertisements
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 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
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 `beta/(aalpha+b)+alpha/(abeta+b)`
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
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)`
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.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
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
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2x^2 + (7/2)x + 3/4`
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
