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skad [1K]
3 years ago
5

What non-zero rational number must be placed in the square so that the simplified product of these two binomials is a binomial:

(7t-10)(5t+Box )? Express your answer as a mixed number.
Mathematics
2 answers:
aleksandrvk [35]3 years ago
7 0

The product would expand to

(7t-10)(5t+x)=35t^2+7tx-50t-10x=35t^2+(7x-50)t-10x

This is a trinomial, and the only way to make it a binomial is to cancel out a coefficient using our variable x.

So, we can cancel either the linear term or the constant term.

In the first case, we require

7x-50=0 \iff 7x=50 \iff x=\dfrac{50}{7}=\dfrac{49}{7}+\dfrac{1}{7}=7\dfrac{1}{7}

In the second case, we require

-10x=0\iff 10x=0 \iff x=0

But x must be a non-zero rational number, so this solution is not feasible.

dimaraw [331]3 years ago
3 0

Answer:

7 1/7.

Step-by-step explanation:

The middle 2 numbers in the expansion will be cancelled out  if one of them is + 50 t so the required  rational number is  50/7:

(7t - 10)(5t + 50/7) = 35t^2 - 50t + 350/7 t - 500/7)

=  35t^2 - 50t + 50t - 500/7)

= 35t^2 - 500/7)

So  50 / 7 = 7 1/7 (answer).

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