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
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 – 24abcdx + 16c2d2 = 0, a ≠ 0, b ≠ 0
If p, q are real and p ≠ q, then show that the roots of the equation (p – q) x2 + 5(p + q) x – 2(p – q) = 0 are real and unequal.
48x² – 13x -1 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
The quadratic equation whose roots are 1:
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
