Answer :
Answer:
[tex]x^{2} -2x-35 =0[/tex] is the equation of solution -5,7.
Step-by-step explanation:
Given : solutions of equation are –5 and 7.
To find : x² + __ x +__ = 0 complete the equation .
Solution : We have given that solutions of equation are -5, 7.
Standard form of quadratic equation [tex]x^{2} +px+q =0[/tex].
Its factors as (x -α) (x- β)
Where , p = −(α + β) and q = αβ.
So, roots are ( x- (-5)) (x-7)
p = -( -5+7) and q =(-5)(7).
p = -2 and q = -35.
On substituting p and q in equation
[tex]x^{2} +(-2)x+(-35) =0[/tex].
[tex]x^{2} -2x-35 =0[/tex].
Therefore, [tex]x^{2} -2x-35 =0[/tex] is the equation of solution -5,7.
The equation that has the solutions -5 and 7 is:
[tex]x^2-2x+35=0[/tex]
Solving quadratic equations
Note that:
The equation with the solutions a and b is given by:
[tex](x-a)(x-b)=0[/tex]
For the equation that has the solutions -5 and 7, the equation is formed as:
[tex](x+5)(x-7)=0[/tex]
Expanding the equation above, we have:
[tex]x^2-7x+5x-35=0\\\\x^2-2x+35=0[/tex]
Therefore, the equation that has the solutions -5 and 7 is:
[tex]x^2-2x+35=0[/tex]
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