Question

*Which one of the following is a quadratic equation?* 1️⃣ (l + 2) (l - 5) = 0 2️⃣ (l + 2)² (l - 5) = 0 3️⃣ (l + 2) (l - 5)² = 0 4️⃣ (l + 2) (l - 5) (l - 9) = 0​

Answer 1

Answer:

Question 2:

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

ANSWER:

(1) x2 + 5x – 2 = 0

Only one variable x.

Maximum index = 2

So, it is a quadratic equation.

(2) y2 = 5y – 10

Only one variable y.

Maximum index = 2

So, it is a quadratic equation.

(3) y2+

1

y

=2

⇒y3+1=2y

Only one variable y.

Maximum index = 3

So, it is not a quadratic equation.

(4) x+

1

x

=-2

⇒x2+1=-2x

Only one variable x.

Maximum index = 2

So, it is a quadratic equation.

(5) (m + 2) (m – 5) = 0

⇒m2-3m-10=0

Only one variable m.

Maximum index = 2

So, it is a quadratic equation.

(6) m3 + 3m2 – 2 = 3m3

Only one variable m.

Maximum index = 3

So, it is not a quadratic equation.

Answer 2

Answer:

Required quadratic equation is (l + 2) (l - 5) = 0.

So, option 1 is the correct answer.

Step-by-step explanation:

We know, quadratic equation is a polynomial equation of a second degree.

By option test , we can find the quadratic equation.

Option -1:

$(l + 2)(l - 5) = 0 \\ {l}^{2} - 5l + 2l - 10 = 0 \\ {l}^{2} - 3l - 10 = 0$

This is a second degree equation.

So, this is a quadratic equation according to rule.

Option -2:

${(l + 2)}^{2} (l - 5) = 0 \\ ( {l}^{2} + 4l + 4)(l - 5) = 0 \\ {l}^{3} + 4 {l}^{2} + 4l - 5 {l}^{2} + 20l + 50 = 0 \\ {l}^{3} - {l}^{2} + 24l + 50 = 0$

This is a third degree equation.

So,this is not a quadratic equation according to rule.

Option -3:

$(l + 2) {(l - 5)}^{2} = 0 \\ (l + 2)( {l}^{2} - 10l + 25) = 0 \\ {l}^{3} - 10 {l}^{2} + 25l + 2 {l}^{2} - 20l + 50 = 0 \\ {l}^{3} - 8 {l}^{2} + 5l + 50 = 0$

This is a third degree equation.

So, this is not a quadratic equation according to rule.

Option -4:

$(l + 2)(l - 5)(l - 9) = 0 \\ ( {l}^{2} - 3l - 10)(l - 9) = 0 \\ {l}^{3} - 3 {l}^{2} - 10l - 9 {l}^{2} + 27l + 90 = 0 \\ {l}^{3} - 12 {l}^{2} + 17l + 90 = 0$

This is a third degree equation.

So, this is not a quadratic equation.

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