Advertisements
Advertisements
Question
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
Solution
3p2 + 8p + 5 = 0
∴ 3p2 + 5p + 3p + 5 = 0
| 3 × 5 = | 15 |
| 5 3 | |
| 5 × 3 = 15 5 + 3 = 8 |
∴ p(3p + 5) + 1(3p + 5) = 0
∴ (3p + 5) (p + 1) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
3p + 5 = 0 or p + 1 = 0
∴ 3p = – 5 or p = – 1
∴ p = `(-5)/3` or p = – 1
∴ The roots of the given quadratic equation are `(-5)/3` and – 1
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by factorization method: 9x2-25 = 0
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
The sum of a number and its square is 63/4. Find the numbers.
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
`2x^2+5x-3=0`
Divide 57 into two parts whose product is 680.
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
Find the values of p for which the quadratic equation
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more then each would have got Rs. 12 less. Find ‘x’.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
(x – 3) (x + 5) = 0 gives x equal to ______.
