Question

Which number can be used to fill in the blank of f(x)=x²+_____x+100 to make a perfect square trimoal. Possible answers a.40 b.20 c.50 d.10 e.100

Answer 1

The missing number in the equation to form a perfect square trinomial should be 20, which is double the product of the square roots of the first and the third terms.

Step-by-step explanation:

In this case, you're working with a quadratic equation of the form ax² + bx + c, and you need to turn the equation f(x)=x²+bx+100 into a perfect square trinomial. The key to this is understanding how perfect square trinomials are formed. In a perfect square trinomial, the middle term (b) is twice the product of the square root of the first term (a) and the last term (c). Therefore, in this equation, the blank would need to be filled with twice the product of the square root of 'x²' (which is x) and the square root of '100' (which is 10). So b = 2*x*10 = 20. Hence, out of the given options, option b. 20 is correct.

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