Find the condition that one root of ax2 + bx + c = 0 may be four times – InterviewSolution

InterviewSolution

1.

Find the condition that one root of ax2 + bx + c = 0 may be four times the other.

Answer»

Let the roots be α and 4α. Then,

α + 4α = 5α = \(-\frac{b}{a}\)

α . 4α = 4α² = \(\frac{c}{a}\)

From (i) α = \(\frac{b}{5a}\)

∴ From (ii) 4. \(\big(-\frac{b}{5a}\big)^2\) = \(\frac{c}{a}\) ⇒ \(\frac{4b^2}{25a^2}\) = \(\frac{c}{a}\) ⇒ 4b² = 25ac.

Discussion

No Comment Found

Related InterviewSolutions

Find the values of k for equation have real rootsx2 – 4kx + k = 0
Decide which of the following are quadratici. x + 1/x = -2 ii. (m + 2) (m – 5) = 03 iii. m3 + 3m2 – 2 = 3m3
Compare the given quadratic equations to the general form and write values of a, b, c.i. x2 – 7x + 5 = 0ii. 2m2 = 5m – 5iii. y2 = 7y
Decide which of the following are quadratic i. x2 – 7y + 2 = 0 ii. y2 = 5y – 10 iii. y2 + 1/y = 2
If a polygon of ‘n’ sides has 1/2 n(n – 3) diagonals. How many sides will a polygon having 65 diagonals? Is there a polygon with 50 diagonals?
Find the nature of the roots of the following quadratic equation. If real roots exist, find them.2x2 – 3x + 5 = 0
The least value of k which makes the roots of the equation x2 + 5x + k = 0 imaginary is A. 4 B. 5 C. 6 D. 7
The degree of a quadratic equation is A) 1 B) 0 C) 2 D) 3
The equation of the smallest degree with real coefficients having 1 + i as one of the roots is A. x2 + x + 1 = 0B. x2 - 2x + 2 = 0C. x2 + 2x + 2 = 0 D x2 + 2x - 2 = 0
If the graph of ax2 + bx + c = 0, a ≠ 0 never intersects X axis then the number of real zeroes are ……………….. A) 2 B) 0 C) 3 D) 4