Advertisements
Advertisements
प्रश्न
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.
उत्तर
Given: `ax2 + 7x + b = 0`
Since, `x=2/3`is the root of the above quadratic equation
Hence, it will satisfy the above equation.
Therefore, we will get ,
`a(2/3)^2+7(2/3)+b=0`
⇒ `4/9a+14/3+b=0`
⇒ `4a+42+9b=0`
⇒ `4a+9b=-42` .............(1)
Since, x = –3 is the root of the above quadratic equation
Hence, It will satisfy the above equation.
Therefore, we will get
`a(-3)^2+7(-3)+b=0`
`⇒ 9a-21+b=0`
`⇒9a+b=21` ......................(2)
From (1) and (2), we get
a = 3, b = –6
APPEARS IN
संबंधित प्रश्न
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case
x3 – 4x2 + 5x – 2; 2, 1, 1
If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
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.
`(-3)/(2sqrt(5)), -1/2`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
Find the zeroes of the polynomial x2 + 4x – 12.
