Advertisements
Advertisements
प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Advertisements
उत्तर
We have
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Here, `a = (4)/(3), b = -2 and c = (3)/(4)`
Discriminant
= b2 - 4ac
= (-2)2 -4 x `(4)/(3) xx (3)/(4)`
= 4 - 4
= 0
So, the given equation has two real and equal roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 + 0)/(4)`
= `(3)/(4)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 - 0)/(2 xx (4)/(3))`
= `(3)/(4)`.
संबंधित प्रश्न
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(k + 1)x + (k + 4) = 0
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
Which of the following equations has two distinct real roots?
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
