Advertisements
Advertisements
Question
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Advertisements
Solution
a2x2 + 2ax + 1 = 0
⇒ a2x2 + ax + ax + 1 = 0
⇒ ax(ax + 1) +1 (ax + 1) = 0
⇒ ax(ax + 1) (ax + 1) = 0
⇒ (ax + 1)2 = 0
∴ ax + 1 = 0 or ax + 1 = 0
⇒ `x = -(1)/a or x = -(1)/a`
Hence x = `-(1)/a "or" x = -(1)/a`.
APPEARS IN
RELATED QUESTIONS
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Solve the following quadratic equation by factorisation:
x2 - 3x - 10 = 0
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
