Question

1. The expression ax^2 + bx takes the value 6 when x = 1 and 10 when x = 2. Find its values when x = 5

Answer 1

Answer:

Expression: ax² + bx

Step-by-step explanation:

a(5)² + b(5)

=25a + 5b

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Answer 2

Concept:

An algebraic expression in mathematics is an expression which is formed from variables and constants, together with algebraic operations (addition, subtraction, etc.).

Given:

we are given an expression $ax^2+bx$ takes the worth $6$ when $x=1$ and $10$ when $x=2$.

Find:

we have to search out the worth when $x=5.$

Solution:

Let us take the given expression as $y=ax^2+bx$.    ....(1)

When $x=1$ then $y=6$ and substitute these values in given expression, we get

$\begin{aligned}6&=a(1)^2+b(1)\\ 6&=a+b\end{aligned}$        ......(2)

When $x=2$ then $y=10$ and substitute these values in given expression, we get

$\begin{aligned}10&=a(2)^2+b(2)\\ 10&=4a+2b\end$       .......(3)

Now, we'll simplify equation (2) and (3), we get

$\begin{aligned}24-10&=4a+4b-4a-2b\\ 14&=2b\\ 7&=b\end$

Further, substitute the worth $b=7$ in equation (2), we get

$\begin{aligned}6&=7+b\\ b&=-1\end$

Furthermore, Substitute the values $a$ and $b$ in equation (1), we get

$y=-a+7b$       ......(4)

Now, we'll find the worth when $x=5$ in equation (4), we get

$\begin{aligned}y&=-5+7(5)\\ y&=-5+35\\ y&=30\end$

Hence, the worth when $x=5$ is $30.$

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