Advertisements
Advertisements
प्रश्न
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
Advertisements
उत्तर
Given equation is 8x2 + 2x – 3 = 0
On comparing with ax2 + bx + c = 0, we get
a = 8, b = 2 and c = – 3
∴ Discriminant, D = b2 – 4ac
= (2)2 – 4(8)(– 3)
= 4 + 96
= 100 > 0
Therefore, the equation 8x2 + 2x – 3 = 0 has two distinct real roots because we know that,
If the equation ax2 + bx – c = 0 has discriminant greater than zero, then it has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-2 +- sqrt(100))/16`
= `(-2 +- 10)/16`
= `(-2 + 10)/16, (-1 - 10)/16`
= `8/16, -12/16`
= `1/2, - 3/4`
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
Solve the following quadratic equation using formula method only :
x2 +10x- 8= 0
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
`10x -(1)/x` = 3
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The quadratic equation whose one rational root is `3 + sqrt2` is
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
