Advertisements
Advertisements
प्रश्न
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
उत्तर
2x2 + x-1=0
b2 - 4ac
= (1)2-4(2)(-1)
= 1+ 8
=9
Since 9 is a perfect square and greater than 0, hence the roots are real and rational.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Find the value of k for which the following equation has equal roots:
(k − 12)x2 + 2(k − 12)x + 2 = 0.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
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 ______.
