Advertisements
Advertisements
प्रश्न
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
उत्तर
Given x4 - 26x2 + 25 = 0
Putting x2 = y, the given equation reduces to the form y2 - 26y + 25 = 0
⇒ y2 - 25y - y + 25 = 0
⇒ y(y - 25) -1(y- 25) = 0
⇒ (y - 25) (y - 1) = 0
⇒ y - 25 = 0 or y - 1 = 0
⇒ y = 25 or y = 1
∴ x2 = 25
⇒ x = ± 5
or
x2 = 1
x = ±1
Hence, the required roots are ±5, ±1.
APPEARS IN
संबंधित प्रश्न
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Find the value of k for which the roots of the equation 3x2 - 10x + k = 0 are reciprocal of each other.
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
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 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.
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
