Advertisements
Advertisements
प्रश्न
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
उत्तर
(x - 1)(2x - 7) = 0
2x2 - 2x - 7x + 7 = o
2x2 - 9x + 7 = o
b2 - 4ac
= (-9)2 - 4(2)(7)
= 81 - 56
= 25
Since discriminant is a perfect square 1 hence the roots are real and rational.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
If the roots of the equation (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
Which of the following equations has the sum of its roots as 3?
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
The roots of quadratic equation x2 – 1 = 0 are ______.
