(C) The curve $y = x^2 + ax + 25$ touches the $x-$axis,which means the quadratic equation $x^2 + ax + 25 = 0$ has equal roots.For equal roots,the disc

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(C) The curve $y = x^2 + ax + 25$ touches the $x-$axis,which means the quadratic equation $x^2 + ax + 25 = 0$ has equal roots.For equal roots,the discriminant $D$ must be zero.$D = b^2 - 4ac = 0$Substituting the values $a=1, b=a, c=25$:$a^2 - 4(1)(25) = 0$$a^2 - 100 = 0$$a^2 = 100$$a = \pm 10$

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

Easy

For what value of $a$ does the curve $y = x^2 + ax + 25$ touch the $x-$axis?

A
$0$
B
$\pm 5$
C
$\pm 10$
D
None of these

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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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If $S = {m \in \mathbb{R} : x^2 - 2(1 + 3m)x + 7(3 + 2m) = 0}$ has distinct roots $\}$,then the number of elements in $S$ is

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The expression $x^2 + 2bx + c$ has a positive value for all real $x$ if:

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For what value of $a$ does the curve $y = x^2 + ax + 25$ touch the $x-$axis?

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Find the complete set of values of $k$ for which the equation $4^x - (k + 2)2^x + 2k = 0$ has exactly one positive root.

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