If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?
Answer Details
Given the quadratic equation: \(x^2 +15x + 50 = ax^2 + bx + c = 0\), where a, b, and c are constants. The question is asking which of the following statements is not true.
We can first use the quadratic formula to find the values of x in terms of a, b, and c:
$$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Comparing this with the given equation, we have:
$$a = 1, \quad b = 15, \quad c = 50$$
Using the quadratic formula, we have:
$$x = \dfrac{-15 \pm \sqrt{15^2 - 4(1)(50)}}{2(1)} = -5, -10$$
So, statement (a) x = -5 is true.
To find out which statement is not true, we can check each option.
Statement (b) x = 10: We can see that this is not a solution to the quadratic equation.
Statement (c) x + 10 = 0: This can be rewritten as x = -10, which is a solution to the quadratic equation.
Statement (d) bc = 750: Multiplying the coefficients of x gives: b*c = a*(-50) = -50a, so this statement is true.
Therefore, the statement that is not true is (b) x = 10.