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Home » Choose the correct answer from the given four options in the following questions: Which of the following is a quadratic equation?
Choose the correct answer from the given four options in the following questions: Which of the following is a quadratic equation?
CBSE | Class 10 | Exercise 4.1 | Maths | NCERT Exemplar | Quadratic Equations
Choose the correct answer from the given four options in the following questions: Which of the following is a quadratic equation?

(A) x2 + 2x + 1 = (4 – x)2 + 3 (B) –2x2 = (5 – x)(2x-(2/5))

(C) (k + 1) x2 + (3/2) x = 7, where k = –1 (D) x3 – x2 = (x – 1)3

(D)

    \[x3\text{ }\text{ }x2\text{ }=\text{ }\left( x\text{ }\text{ }1 \right)3\]

Clarification:

The standard type of a quadratic condition is given by,

    \[ax2\text{ }+\text{ }bx\text{ }+\text{ }c\text{ }=\text{ }0,\text{ }a\text{ }\ne \text{ }0\]

(A) Given,

    \[x2\text{ }+\text{ }2x\text{ }+\text{ }1\text{ }=\text{ }\left( 4\text{ }\text{ }x \right)2\text{ }+\text{ }3\]

    \[x2\text{ }+\text{ }2x\text{ }+\text{ }1\text{ }=\text{ }16\text{ }\text{ }8x\text{ }+\text{ }x2\text{ }+\text{ }3\]

    \[10x\text{ }\text{ }18\text{ }=\text{ }0\]

which is certifiably not a quadratic condition.

(B) Given,

    \[-\text{ }2x2\text{ }=\text{ }\left( 5\text{ }\text{ }x \right)\text{ }\left( 2x\text{ }\text{ }2/5 \right)\]

    \[-\text{ }2x2\text{ }=\text{ }10x\text{ }\text{ }2x2\text{ }\text{ }2\text{ }+2/5x\]

    \[52x\text{ }\text{ }10\text{ }=\text{ }0\]

which is certainly not a quadratic condition.

(C) Given,

    \[\left( k\text{ }+\text{ }1 \right)\text{ }x2\text{ }+\text{ }3/2\text{ }x\text{ }=\text{ }7\]

, where k = – 1

    \[\left( -\text{ }1\text{ }+\text{ }1 \right)\text{ }x2\text{ }+\text{ }3/2\text{ }x\text{ }=\text{ }7\]

    \[3x\text{ }\text{ }14\text{ }=\text{ }0\]

which is anything but a quadratic condition.

(D) Given,

    \[x3\text{ }\text{ }x2\text{ }=\text{ }\left( x\text{ }\text{ }1 \right)3\]

    \[x3\text{ }\text{ }x2\text{ }=\text{ }x3\text{ }\text{ }3x2\text{ }+\text{ }3x\text{ }\text{ }1\]

    \[2x2\text{ }\text{ }3x\text{ }+\text{ }1\text{ }=\text{ }0\]

which addresses a quadratic condition.

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