Decide which of the following are quadratic equations.
(1)x²+5x-2 = 0
(2)y²=5y-10
(3)y²+1/y=2
(4)x+1/x =-2
(5)(m+2)(m-5)=0
(6)m³+3m²-2=3m³
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A equation is known as quadratic when it is in the form of ax² + bx + c = 0 , where a ≠ 0 . I mean every two degree polynomial is known as quadratic equation.
now, Let's check all of these.
(1) it is quadratic because it is in the form of ax² + bx + c = 0 where a = 1 ≠ 0
(2) it is too quadratic because it is in the form of ax² + bx + c = 0 where a = 1 ≠ 0
(3) it is not quadratic because it is not in the form of ax² + bx +c = 0.
if you resolve y² + 1/y = 2 , you will get y³ -2y + 1= 0 which is 3rd degree polynomial.
(4) it is quadratic ,let see how ,
x + 1/x = -2
(x² + 1)/x = -2
x² + 1 + 2x = 0
x² + 2x + 1 = 0 , it is in the form of ax² + bx + c =0. hence, it is quadratic .
(5) (m + 2)(m -5) = 0
m² + 2m - 5m -10 = 0
m² - 3m - 10 = 0, it is in the form of ax² + bx + c = 0 hence, it is quadratic.
(6) it's not ,because it is 3rd degree polynomial as you can see.
now, Let's check all of these.
(1) it is quadratic because it is in the form of ax² + bx + c = 0 where a = 1 ≠ 0
(2) it is too quadratic because it is in the form of ax² + bx + c = 0 where a = 1 ≠ 0
(3) it is not quadratic because it is not in the form of ax² + bx +c = 0.
if you resolve y² + 1/y = 2 , you will get y³ -2y + 1= 0 which is 3rd degree polynomial.
(4) it is quadratic ,let see how ,
x + 1/x = -2
(x² + 1)/x = -2
x² + 1 + 2x = 0
x² + 2x + 1 = 0 , it is in the form of ax² + bx + c =0. hence, it is quadratic .
(5) (m + 2)(m -5) = 0
m² + 2m - 5m -10 = 0
m² - 3m - 10 = 0, it is in the form of ax² + bx + c = 0 hence, it is quadratic.
(6) it's not ,because it is 3rd degree polynomial as you can see.
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X2 + 5 x minus 2 is equal to zero
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