Advertisements
Advertisements
Question
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
Advertisements
Solution
4(2x – 3)2 – (2x – 3) – 14 = 0
Let 2x – 3 = y
Then 4y2 – y – 14 = 0
⇒ 4y2 – 8y + 7y – 14 = 0
⇒ 4y(y – 2) + 7(y – 2) = 0
⇒ (y – 2)(4y + 7) = 0
If y – 2 = 0 or 4y + 7 = 0
⇒ y = 2 or y = `(-7)/4`
⇒ 2x – 3 = 2 or 2x – 3 = `(-7)/4`
⇒ 2x = 5 or 2x = `5/4`
⇒ x = `5/2` or x = `5/8`
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Solve the following equation by factorisation :
2x2 + ax – a2= 0
