Advertisements
Advertisements
Question
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Advertisements
Solution
`f(x) = 2x^2 ˗ 11x + 15`
=` 2x^2 ˗ (6x + 5x) + 15`
`= 2x_2 ˗ 6x ˗ 5x + 15`
`= 2x (x ˗ 3) ˗ 5 (x ˗ 3)`
`= (2x ˗ 5) (x ˗ 3)`
∴ `f(x) = 0 ⇒ (2x ˗ 5) (x ˗ 3) = 0`
⇒ `2x ˗ 5= 0 or x ˗ 3 = 0`
` ⇒ x=5/2 or x=3`
So, the zeroes of f(x) are `5/2 and 3`
Sum of zeroes=`5/2+3=(5+6)/2=11/2 = -(("Coefficient of x"))/(("Coefficient of" x^2))`
Product of zeroes `=5/2xx3=(-15)/2= ("Constant term")/(("Coefficient of"x^2))`
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
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 `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 f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
What will be the expression of the polynomial?
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`21/8, 5/16`
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.
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
