Best methemetics algebra question answer

Algebra Question Answer for 10th Class


Question:

Solve the quadratic equation 2x2−4x−6=02x^2 - 4x - 6 = 02x2−4x−6=0.

Solution:

To solve the quadratic equation, you can use the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

For the given equation 2x2−4x−6=02x^2 - 4x - 6 = 02x2−4x−6=0, the coefficients are:

a=2,b=−4,c=−6a = 2, \quad b = -4, \quad c = -6a=2,b=−4,c=−6

Substitute the values into the quadratic formula:

x=−(−4)±(−4)2−4(2)(−6)2(2)x = \frac{-(-4) \pm \sqrt{(-4)^2 -
4(2)(-6)}}{2(2)}x=2(2)−(−4)±(−4)2−4(2)(−6)​​

Simplify:

x=4±16+484x = \frac{4 \pm \sqrt{16 + 48}}{4}x=44±16+48​​x=4±644x = \frac{4 \pm
\sqrt{64}}{4}x=44±64​​x=4±84x = \frac{4 \pm 8}{4}x=44±8​

So, the two possible solutions are:

x1=4+84=124=3x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3x1​=44+8​=412​=3 x2=4−84=−44=−1x_2 =
\frac{4 - 8}{4} = \frac{-4}{4} = -1x2​=44−8​=4−4​=−1

Final Answer: The solutions are x=3x = 3x=3 and x=−1x = -1x=−1.

4o