Advertisements
Advertisements
प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
Determine the nature of the roots of the following quadratic equation:
2x2 - 3x + 5 = 0
उत्तर
Consider the equation
x2 - 3x + 5 = 0
Comparing it with ax2 + bx + c = 0, we get
a = 2, b = -3 and c = 5
Discriminant = b2 - 4ac
= (-3)2 - 4 (2) (5)
= 9 - 40
= -31
As b2 - 4ac < 0,
Therefore, no real root is possible for the given equation.
संबंधित प्रश्न
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(5 + 2k)x + 3(7 + 10k) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
x2 + 4x + 5 = 0
Solve x2/3 + x1/3 - 2 = 0.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Which of the following equations has 2 as a root?
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
A quadratic equation with integral coefficient has integral roots. Justify your answer.
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Solve for x: 9x2 – 6px + (p2 – q2) = 0
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
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.
