Question

It is given that the areas of the rectangle and square are same. Then which of the following quadratic equation is true?Required to answer. Single choice.

(1 Point)

x² + 2x + 8 = 0

x² + 2x - 8 = 0

x² - 2x + 8 = 0

x² - 2x + 8 = 0

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Answer 1

Step-by-step explanation:

(i) x2−2x−8=0

x2−4x+2x−8=0

x(x−4)+2(x−4)=0

(x+2)(x−4)=0

⟹x=−2,4

(ii) The equation is of the form ax2+bx+c=0 where:

a=1,b=2,c=−8

The Discriminant is given by:

Δ=b2−4⋅a⋅c

=(2)2−(4⋅1⋅(−8))

=4+32=36

The solutions are found using the formula

x=−b±√Δ2⋅a

x=(−2)±√36)2⋅1=(−2±6)2

x=−2+62=42=2 , x=2

x=−2−62=−82=−4 , x=−4

The equation is of the form ax2+bx+c=0 where:

a=1,b=2,c=−8

The Discriminant is given by:

Δ=b2−4⋅a⋅c

=(2)2−(4⋅1⋅(−8))

=4+32=36

The solutions are found using the formula

x=−b±√Δ2⋅a

x=(−2)±√36)2⋅1=(−2±6)2

x=−2+62=42=2 , x=2

x=−2−62=−82=−4 , x=−4