Advertisements
Advertisements
प्रश्न
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
विकल्प
p < `(9)/(2)`
p ≤ `(9)/(2)`
p > `(9)/(2)`
p ≥ `(9)/(2)`
Advertisements
उत्तर
2x² – 6x + p = 0
Here, a = 2, b = –6, c = p
b2 – 4ac
= (–6)2 – 4 x 2 x p
= 36 – 8p
∵ Roots are real and unequal.
∴ b2 – 4ac > 0
⇒ 36 – 8p > 0
⇒ 36 > 8p
⇒ `(36)/(8)` > p
⇒ p < `(36)/(8)`
⇒ p < `(9)/(2)`.
APPEARS IN
संबंधित प्रश्न
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
Without solving, examine the nature of roots of the equation 2x2 – 7x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
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
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
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.
