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4 years ago

Jamal started writing thank-you notes at 5:25. It took him 20 minutes to write them.

1 answer:

6 0

Step One: (Jamal started writing thank-you notes at 5:25. It took him 20 minutes to write them.) So Jamal wrote thank you notes until 5:45

Step Two: He also spent some time writing addresses 6:00.

Answer: If you are asking how long it took after 5:45, the answer will be 15 Minutes because 5:45 + 0:15 = 5:60 and since 60 minutes is 1 hour, you have 6:00

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3 years ago

If α and β are the zeroes of the polynomial 6y 2 − 7y + 2, find a quadratic polynomial whose zeroes are 1 α and 1 β .

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$2y^2-7y+6=0$

Step-by-step explanation:

We are given that $\alpha$ and $\beta$ are the zeroes of the polynomial $6y^2-7y+2$

$y^2-\frac{7}{6}y+\frac{1}{3}$

We have to find a quadratic polynomial whose zeroes are $1/\alpha$ and $1/\beta$ .

General quadratic equation

$x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes$

We get

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$\alpha \beta=\frac{1}{3}$

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}$

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}$

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2$

$\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}$

$\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3$

Substitute the values

$y^2-(7/2)y+3=0$

$2y^2-7y+6=0$

Hence, the quadratic polynomial whose zeroes are $1/\alpha$ and $1/\beta$ is given by

$2y^2-7y+6=0$

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