SOLUTION: Write a quadratic equation in standard form with the roots. a) 3+√2 and 3-√2, passes through point (3,1) b) -1+2√3 and -1-2√3, passes through point (-1,4)

Question 1118785: Write a quadratic equation in standard form with the roots.
a) 3+√2 and 3-√2, passes through point (3,1)
b) -1+2√3 and -1-2√3, passes through point (-1,4)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Here is help for (a) only.

Solve the formula for a.

Substitute the given point.

Substitute for the now found value of a in the factored form.

From that, continue to simplify to get the 'standard' form you want.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The purely algebraic method used by the other tutor is fine; however, with the roots 3+sqrt(2) and 3-sqrt(2), the algebra gets a bit messy.

There is a much easier path to the answers.

In the quadratic equation

the sum of the roots is -b/a and the product of the roots is c/a. Then we can write the equation as

In your first example, the sum of the roots is 6 and the product is 9-2=7. So an equation of the parabola is

Then you can find the value of a by substituting the (x,y) values of the given point on the parabola:

And the whole equation is

Then of course use the same method on your second example, where the sum of the roots is -2 and their product is 1-12 = -11.
RELATED QUESTIONS
Write as a polynomial equation with the roots a) -1 , 2 + √(3), 2 - √(3)... (answered by josgarithmetic)
Write a quadratic function for the parabola that passes through the point (2, -3) with... (answered by josgarithmetic)
Write the equation of the line that passes through (-1, 4) with a slope of -1 in standard (answered by Alan3354)
Write the equation of the line which passes through (1, 2) and with slope of -1/3 in... (answered by Fombitz)
Write a quadratic equation with -1/3 and 4 as its roots. Write the equation in standard... (answered by josgarithmetic,MathTherapy)
how do you do variables in square roots and help me with this in simplest radical form... (answered by edjones)
Write a quadratic equation in standard form that has the roots of -3 and... (answered by solver91311)
The function f(x)=a√(x-h) +k has a maximal domain of [2, ∞) and range of (-... (answered by MathLover1,yongweizhen)
Find a polynomial with smallest degree with rational coefficients that has roots (2 -... (answered by t0hierry)

SOLUTION: Write a quadratic equation in standard form with the roots. a) 3+&#8730;2 and 3-&#8730;2, passes through point (3,1) b) -1+2&#8730;3 and -1-2&#8730;3, passes through point (-1,4)

SOLUTION: Write a quadratic equation in standard form with the roots. a) 3+√2 and 3-√2, passes through point (3,1) b) -1+2√3 and -1-2√3, passes through point (-1,4)