Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial `(8x^2 ˗ 4)` and verify the relation between the zeroes and the coefficients
Advertisements
उत्तर
We have:
`f(x)=8x^2-4`
It can be written as `8x^2+o x -4`
=`4{(sqrt2x)^2-(1)^2}`
=`4(sqrt2x+1) (sqrt2x-1)`
∴ `f(x)=0⇒ (sqrt2x+1) (sqrt2x-1)=0`
⇒ `(sqrt2x+1)=0 or sqrt2x-1=0`
⇒ `x=(-1)/sqrt2 or x=1/sqrt2`
So, the zeroes of f(x) are `(-1)/sqrt2 and 1/sqrt2`
Here the coefficient of x is 0 and the coefficient of `x^2` is `sqrt2`
Sum of zeroes = `-1/sqrt2+1/sqrt2=(-1+1)/sqrt2=0/sqrt2=-(("Coefficent of x"))/(("Coefficient of" x^2))`
Product of zeroes=`-1/sqrt2xx1/sqrt2=(-1xx4)/(2xx4)=-4/8=("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:
t2 – 15
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
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 f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
The number of polynomials having zeroes as –2 and 5 is ______.
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.
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
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`
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)`
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.
