Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial (3x2 – x – 4) and verify the relation between the zeroes and the coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
3x2 – x – 4
Advertisements
उत्तर
3x2 – x – 4 = 0
⇒ 3x2 – 4x + 3x – 4 = 0
⇒ x(3x – 4) + 1(3x – 4) = 0
⇒ (3x – 4) (x + 1) = 0
⇒ (3x – 4) or (x + 1) = 0
⇒ `x = 4/3` or x = –1
Sum of zeroes = `4/3 + (-1)`
= `1/3`
= `(-("Coefficient of" x))/(("Coefficient of" x^2))`
Product of zeroes = `4/3 xx (-1)`
= `(-4)/3`
= `("Constant term") /(("Coefficient of "x^2))`
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
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 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 α2β + αβ2
If a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
If one zero of the quadratic polynomial f(x) = 4x2 − 8kx − 9 is negative of the other, find the value of k.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`
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)`
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
If 3 and –3 are two zeroes of the polynomial (x4 + x3 – 11x2 – 9x + 18), find all the zeroes of the given polynomial.
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
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:
4x2 – 3x – 1
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
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.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
