(×+3)(×+5)_>×+2 what is the answer of this equation
Answer (1)
Answer:All real numbersStep-by-step explanation:1. Expand the left side:x^2 + 5x + 3x + 15 > x + 2x^2 + 8x + 15 > x + 22. Move all terms to the left side:x^2 + 8x - x + 15 - 2 > 0x^2 + 7x + 13 > 03. Find the roots of the quadratic equation x^2 + 7x + 13 = 0 using the quadratic formula:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}Where a = 1, b = 7, and c = 13.4. Substitute the values into the formula:x = \frac{-7 \pm \sqrt{7^2 - 4(1)(13)}}{2(1)}x = \frac{-7 \pm \sqrt{49 - 52}}{2}x = \frac{-7 \pm \sqrt{-3}}{2} Since the discriminant (b^2 - 4ac) is negative (-3), there are no real roots. This means the quadratic expression does not cross the x-axis. Since the coefficient of x^2 is positive (1), the parabola opens upwards. Because there are no real roots, the parabola is always above the x-axis. Therefore, x^2 + 7x + 13 is always positive for all real values of x. Thus, the solution to the inequality x^2 + 7x + 13 > 0 is:All real numbers.
