Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
Advertisements
उत्तर
We have:
`f(x) = x^2 ˗ 5`
It can be written as ` x^2+ o x-5`
=`(x^2-(sqrt5)^2)`
=`(x+sqrt5) (x-sqrt5)`
∴` f(x)=0⇒ (x+sqrt5) (x-sqrt5)=0`
`⇒ x+sqrt5=0 or x-sqrt5=0`
`⇒x=-sqrt5 or x=sqrt5`
So, the zeroes of f(x) are `-sqrt5 and sqrt5`
Here, the coefficient of x is 0 and the coefficient of `x^2 `is 1.
Sum of zeroes=-`sqrt5+sqrt5=0/1=-(("Coefficient of x"))/(("Coefficient of "x^2))`
Product of zeroes`=-sqrt5xxsqrt5=(-5)/1= ("Constant term")/(("Coefficient of" x^2))`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
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) = ax2 + bx + c, then evaluate α - β
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
If α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`
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 a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively.
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
Define a polynomial with real coefficients.
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
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 quadratic polynomial x2 + 99x + 127 are ______.
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
Find the zeroes of the polynomial x2 + 4x – 12.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
