PLEASE HELPP Find quadratic equation with integral coefficients that has the given roots pleasee

9514 1404 393

  y = x² -8x +13

Step-by-step explanation:

Put the roots in the intercept form and multiply it out. For roots p and q, the quadratic is ...

  y = (x -p)·(x -q)

  y = (x -(4+√3)) · (x -(4 -√3))

  y = ((x -4) -√3) · ((x -4) +√3) = (x -4)² -(√3)² . . . . use the special product form

  y = x² -8x +16 -3 . . . . use the other special product form

  y = x² -8x +13

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Comment on the special product

There are a couple of quadratic special products that are useful to remember:

  the difference of squares: (a -b)(a +b) = a² -b²

  the square of a sum: (a + b)² = a² +2ab +b²

When working with quadratics that have complex or radical conjugate roots, the difference of squares form comes in handy sometimes.

Math can be a lot easier if you learn to recognize and use patterns.

answer: ouch. thats difficult

step-by-step explanation:

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1