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2 years ago

Write a quadratic function with zeros -1 and 5.

Mathematics

1 answer:

Shalnov [3]2 years ago

3 0

Answer:

$x^2+4x-5$

Step-by-step explanation:

Zeros of a quadratic equation are -1 and 5.

Sum of zeros = -1 + 5 = 4

Product of zeros = (-1)(5) = -5

The quadratic equation will be :

$x^2+(\text{sum of zeros})x+\text{product of zeros}\\\\=x^2+4x-5$

So, the required quadratic equation is $x^2+4x-5$ .

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2 years ago

Select the two values of x that are roots of this equation 3x^2 + 1 =5x

Zina [86]

Answer:

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Step-by-step explanation:

To find the root of the equation stated above we need to:

(1) Write the polynomial equation with zero on the right hand side:

$3x^{2} + 1 = 5x$ ⇒ $3x^{2} -5x + 1 = 0$

(2) Divide the whole equation by 3

$3x^{2} -5x + 1 = 0$ ⇒ $x^{2} -\frac{5}{3}x + \frac{1}{3}= 0$

(3) Use the quadratic formula to solve the quadratic equation:

The quadratic formula states that the two solutions for a quadratic equation is given by:

$\frac{-b±\sqrt{b^{2} - 4ac}}{2a}$ (1)

In this case, a = 1, b = $-\frac{5}{3}, c= \frac{1}{3}$

Substituiting a, b and c in equation (1) We get:

$\frac{-\frac{5}{3}±\sqrt{(-\frac{5}{3})^{2} - 4(1)(\frac{1}{3})}}{2(1)}$ (1)

The two solutions are:

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2 years ago