You've got a=4
-b/a=sum=-1+6=5 so b=-20
c/a=product=-1*6=-6 so c=-6
Final equation: 4 x 2 − 20 x − 6 = 0
The quadratic equation is 4x² - 20x - 24 = 0 whose roots are-1 and 6.
What is a quadratic equation?
The quadratic equation is defined as a function containing the highest power of a variable is two.
The roots are given in the question, as follows:
-1 and 6
As we know that the standard quadratic equation ax² + b x + c = 0.
Since the leading coefficient of the quadratic equation is 4
So, a = 4
The sum of roots = -b/a
-1 + 6 = -b/4
5 = -b/4
b = -20
The multiplication of roots = c/a
-1 × 6 = c/4
c = -24
So, the quadratic equation is 4x² - 20x - 24 = 0.
Learn more about quadratic function here:
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The quadratic equation with roots -1 and 6, and a leading coefficient of 4 is 4 x 2 − 20 x − 24 = 0 . This is derived by using the factored form of the quadratic and expanding it. The process involves substituting the roots into the equation and simplifying it to standard form.
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[tex]9 \div 1.5 \\ = \frac{9}{1} \div \frac{15}{10} \\ \\ = \frac{9}{1} \times \frac{10}{15} \\ \\ = \frac{90}{15} = 6[/tex]