Question

6x

सिक्स एक्स स्क्वायर प्लस 5 एक्स माइनस 4 इज इक्वल टू जीरो

​

Answer 1

Answer:

How do you solve the following quadratic equation: 6x^2 + 5x - 4 = 0?

Solution: 6x^2 + 5x - 4 = 0

Here is the method to go about solving similar quadratic equations.

The product of 6 and 4 = 24.

Find factors of 24, such that their difference (D) is 5:

1, 24. D = 23. Fail

2, 12. D = 10. Fail.

3, 8. D = 5. Right.

4, 6. D = 2. Fail.

So write 6x^2 + 5x - 4 = 0 as

6x^2+8x-3x-4 = 0

(6x^2+8x)-(3x+4) = 0

2x(3x+4) - (3x+4) = 0

(2x-1)(3x+4) = 0.

Either (2x-1) = 0, or (3x+4) = 0, hence

x = 1/2 or -4/3. Answer.

Check: 6x^2 + 5x - 4 = 0

f(1/2): LHS = 6/4 +5/2 - 4

= 3/2+5/2 -8/2

= 0 = RHS. Correct

6x^2 + 5x - 4 = 0

f(-4/3): LHS = 96/9 -20/3 - 4

= 96/9-60/9 -36/9

= 0 = RHS. Correct.

Answer 2

$\\ 6 {x}^{2} + 5x - 4 = 0$

${\bf{\large{\underline{\underline{Solving \; the \; equation:-}}}}}$

$\\ 6 {x}^{2} + 5x - 4 = 0 \\ \\ = > 6 {x}^{2} - 3x + 8x - 4 = 0 \\ \\ = > 3x(2x - 1) + 4(2x - 1) = 0 \\ \\ = > (3x + 4) \times (2x - 1) = 0 \\ \\ = > 3x + 4 = 0 \\ = > x = \frac{ - 4}{3} \\ \\ or \\ \\ = > 2x - 1 = 0 \\ = > x = \frac{ - 1}{2}$