A polynomial function M is defined as M(x)=(2x-3)(x^(2)+3x+10) If M(a)=0 for some real number a, then what is the value of a ?

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A polynomial function  M is defined as  M(x)=(2x-3)(x^(2)+3x+10) If  M(a)=0 for some real number  a, then what is the value of  a ?

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Given Polynomial Function: We are given the polynomial function M(x) = (2x-3)(x^2+3x+10). To find the value of a such that M(a) = 0, we need to set the function equal to zero and solve for x.Factors of M(x): The function M(x) is the product of two factors: (2x-3) and (x^2+3x+10). For the product to be zero, at least one of the factors must be zero.Setting Linear Factor to Zero: First, let's set the linear factor equal to zero and solve for x: 2x - 3 = 0. Adding 3 to both sides gives us 2x = 3. Dividing both sides by 2 gives us x = 3/2.Solving the Quadratic Factor: Now, let's consider the quadratic factor: x^2 + 3x + 10 = 0. This is a quadratic equation, and we can attempt to solve it using the quadratic formula, factoring, or completing the square. However, we can also check the discriminant (b^2 - 4ac) to see if there are real solutions. For this quadratic, a = 1, b = 3, and c = 10.Checking the Discriminant: The discriminant is b^2 - 4ac = (3)^2 - 4(1)(10) = 9 - 40 = -31. Since the discriminant is negative, there are no real solutions to the quadratic equation x^2 + 3x + 10 = 0.Real Solutions for M(x): Since the quadratic factor does not have real solutions, the only real solution for M(x) = 0 comes from the linear factor 2x - 3 = 0, which we solved as x = 3/2. Therefore, the value of a for which M(a) = 0 is a = 3/2.

A polynomial function $M$ is defined as $\newline$ $M(x)=(2 x-3)\left(x^{2}+3 x+10\right)$ $\newline$ If $M(a)=0$ for some real number $a$ , then what is the value of $a$ ?

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A polynomial function M M M is defined as\newlineM(x)=(2x−3)(x2+3x+10) M(x)=(2 x-3)\left(x^{2}+3 x+10\right) M(x)=(2x−3)(x2+3x+10)\newlineIf M(a)=0 M(a)=0 M(a)=0 for some real number a a a, then what is the value of a a a ?

A polynomial function $M$ is defined as $\newline$ $M(x)=(2 x-3)\left(x^{2}+3 x+10\right)$ $\newline$ If $M(a)=0$ for some real number $a$ , then what is the value of $a$ ?