SOLUTION: Find the values of a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 5-√26 and 5+ √26. (Hint: Use the zero-product property in reverse.)

Question 1192005: Find the values of a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 5-√26 and 5+ √26.
(Hint: Use the zero-product property in reverse.)
a=
b=
c=
(Type an integer or a simplified faction.)
Thank you so much for your help!(:
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll use a different approach instead of the hint given.
If you prefer the hint route, then let me know and I'll fix my solution.

and are the two given roots or x intercepts.

For each equation, subtract 5 from both sides
and

If we square both sides, then each right hand side yields 26.
The squaring operation and square root cancel out.
So we have this equation

Let's get it into standard form ax^2+bx+c = 0

Comparing this to ax^2+bx+c = 0, we have
a = 1
b = -10
c = -1

To verify the answers, let's use the quadratic formula to plug in those a,b,c values
We should get the roots your teacher gave you

or
We've confirmed the answers.

Answers:
a = 1
b = -10
c = -1

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

We can assume at the start that a=1; if that leads to values of b and/or c that are not integers, we can scale up our answer.

If a is 1, then b is the opposite of the sum of the roots, and c is the product of the roots.

The sum of the roots is 10.

The product of the roots is 25-26=-1.

ANSWERS:
a=1
b=-10
c=-1

RELATED QUESTIONS
A quadratic equation {{{ ax^2+bx+c=0 }}} has -10 and 5 as solutions. Find the values of b (answered by josgarithmetic)
Find the values of a, b, and c for which the quadratic equation ax^2+bx+c=0 has the... (answered by math_tutor2020)
How do I find a quadratic equation that has -6 and 4 as solutions in the form of... (answered by ankor@dixie-net.com)
How do you find real numbers a,b and c so that the graph of the function {{{ y=ax^2+bx+c... (answered by josgarithmetic,MathTherapy)
Dealing with contradictions: If a, b, and c are nonzero real numbers such that a>0 and... (answered by venugopalramana)
Find the values of a, b, and c such that the equation y = ax2 + bx + c has ordered pair... (answered by MathLover1)
A quadratic equation x^2+bx+c=0 has the complex roots 3+6i and 3-6i. Find the values of b (answered by richwmiller)
{{{(3x)/(2x+5)-(5x+2)/(2x-5)=(Ax^2+Bx+C)/((2x+5)(2x-5))}}} Find the smallest values of (answered by ankor@dixie-net.com)
Find an equation where ax^2+bx+c=0 with solutions of 2/5 and... (answered by nerdybill)

SOLUTION: Find the values of​ a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 5-√26 and 5+ √26. ​(Hint: Use the​ zero-product property in​ reverse.)

SOLUTION: Find the values of a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 5-√26 and 5+ √26. (Hint: Use the zero-product property in reverse.)