(C) quadratic equation is of the form $ax^2 + bx + c = 0$,where $a \neq 0$.Since one root is $0$,the constant term $c$ must be $0$.Thus,the equation i

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(C) quadratic equation is of the form $ax^2 + bx + c = 0$,where $a \neq 0$.Since one root is $0$,the constant term $c$ must be $0$.Thus,the equation is $ax^2 + bx = 0$,where $a, b \in \{0, 1, 2, \dots, 9\}$ and $a \neq 0$.The number of choices for $a$ is $9$ (as $a \in \{1, 2, \dots, 9\}$).The number of choices for $b$ is $10$ (as $b \in \{0, 1, 2, \dots, 9\}$).Therefore,the total number of such quadratic equations is $N = 9 \times 10 = 90$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $N$ denotes the number of quadratic equations with coefficients from the set $\{0, 1, 2, \dots, 9\}$ such that one root is $0$,then the value of $N$ is:

A
$29$
B
Infinite
C
$90$
D
$900$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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DifficultAIEEE 2012

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If $N$ denotes the number of quadratic equations with coefficients from the set $\{0, 1, 2, \dots, 9\}$ such that one root is $0$,then the value of $N$ is:

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