Question

What should be added to 3x
$what \: should \: be \: added \: to \: 3x {?}^{2} - 6x - 7to \: make \: 4x {?}^{2} + x - 2$
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Answer 1

Given :

Two expressions $3x^{2} -6x-7$ and $4x^{2} +x-2$

To find :

What should be added to $3x^{2} -6x-7$ to get $4x^{2} +x-2$

Step-by-step explanation:

• Let the quadratic equations be $ax^{2} +bx+c$ and $px^{2} +qx+r$
• The addition of two quadratic equations resulting to another quadratic equation can be written in the form of
• Where the resultant quadratic equation is already given.
• So, the equation can be written as

        $4x^{2} +x-2 = (ax^{2} +bx+c)+(px^{2} +qx+r)$

• From the given datas, we know one quadratic equation.
• In order to find the other equation , take this expression to the other side of the equation.
• Substitute the given values
• Then, the equation will become

        $4x^{2} +x-2 = 3x^{2} -6x-7+(px^{2} +qx+r)$

• Take the expression to the other side of the equation

        $4x^{2} +x-2-3x^{2} +6x+7=px^{2} +qx+r$

• The co efficient must be subtracted correspondingly

         $x^{2} +7x+5=px^{2} +qx+r$

Final answer :

$x^{2} +7x+5$ must be added to $3x^{2} -6x-7$ to get $4x^{2} +x-2$.