(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Solution of quadratic equations and Nature of roots

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then the set of possible values of $a$ is

DifficultAIEEE 2007

View Solution

The equation $(\cos p - 1) x^2 + (\cos p) x + \sin p = 0$ in the variable $x$ has real roots. Then $p$ can take any value in the interval

EasyMHT CET 2024

View Solution

If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

Medium

View Solution

If the roots of $x^4-10x^3+37x^2-60x+36=0$ are $\alpha, \alpha, \beta, \beta$ with $\alpha < \beta$,then find the value of $2\alpha+3\beta-2\alpha\beta$.

EasyTS EAMCET 2018

View Solution

The polynomial $x^2-6x+12 \in \mathbb{Q}[x]$ is

MediumAP EAMCET 2020

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then the set of possible values of $a$ is

The equation $(\cos p - 1) x^2 + (\cos p) x + \sin p = 0$ in the variable $x$ has real roots. Then $p$ can take any value in the interval

If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

If the roots of $x^4-10x^3+37x^2-60x+36=0$ are $\alpha, \alpha, \beta, \beta$ with $\alpha < \beta$,then find the value of $2\alpha+3\beta-2\alpha\beta$.

The polynomial $x^2-6x+12 \in \mathbb{Q}[x]$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module