Advertisements
Advertisements
Question
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
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 zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
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.
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
The product of the zeros of x3 + 4x2 + x − 6 is
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
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 quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
