Advertisements
Advertisements
Question
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Every quadratic equation has at least one real root.
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 ______.
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
