Determine the quadratic equation with roots

Mathematics

1 answer:

zvonat [6]3 years ago

4 0

Answer:

$y=6x^2-5x+1$

Step-by-step explanation:

If the quadratic equation has a root at $\dfrac13$ then when $x=\dfrac13$ , $y=0$

$\implies x=\dfrac13$

$\implies 3x=1$

$\implies 3x-1=0$

If the quadratic equation has a root at $\dfrac12$ then when $x=\dfrac12$ , $y=0$

$\implies x=\dfrac12$

$\implies 2x=1$

$\implies 2x-1=0$

Therefore, $y=(3x-1)(2x-1)$

$\implies y=6x^2-5x+1$

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Add 1/4 + 5/14 +6/7 Simplify the answer and write it as a mixed number.

zhannawk [14.2K]

Answer:

$\frac{41}{28}$ = $1\frac{13}{28}$

Step-by-step explanation:

In order to add fractions, the denominators must all be the same value (the lowest common denominator). The lowest common denominator is the smallest value that all of the given denominators (in this case, the denominators are 4, 14, and 7) can divide into.

Here, the smallest number that all three of the given denominators can perfectly divide into is 28:

28 ÷ 4 = 7

28 ÷ 14 = 2

28 ÷ 7 = 4

Therefore, our lowest common denominator is 28.

The next step is to change our numerators to match our lowest common denominator. To do this, we have to multiply the numerator by the same value that we would need to multiple the denominator by in order to get our lowest common denominator.

For our first term of 1/4, we need to multiply our denominator (4) by 7 in order to get our lowest common denominator of 28. So, we need to also multiply our numerator by 7:

$\frac{1}{4}$ × $\frac{7}{7}$ = $\frac{7}{28}$