Question

Find the value of p, if the following quadratic
equation has equal roots : 4x2 - (p - 2)x + 1 = 0​

Answer 1

Answer:

Here is your answer mate,

Step-by-step explanation:

Please check the attachment

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Answer 2

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given Equation:

$\rm :\longmapsto 4x^{2}-(p - 2)x+1=0$

Comparing it with ax² + bx + c = 0, we get:

$\rm :\longmapsto \begin{cases}\rm a=4\\ \rm b = -(p - 2)\\ \rm c=1\end{cases}$

Discriminant is calculated by using the formula given below:

$\rm :\longmapsto Discriminant=b^{2}-4ac$

Here:

$\rm :\longmapsto D=(2-p)^{2} - 4\times 4\times 1$

$\rm :\longmapsto D=p^{2} - 4p + 4- 16$

$\rm :\longmapsto D=p^{2} - 4p - 12$

As the roots of the given equation are real, discriminant is zero:

$\rm :\longmapsto p^{2} - 4p - 12=0$

$\rm :\longmapsto p^{2} - 6p + 2p - 12=0$

$\rm :\longmapsto p(p - 6) + 2(p - 6) =0$

$\rm :\longmapsto (p + 2)(p - 6) =0$

$\rm :\longmapsto \begin{cases}\rm p + 2=0\\ \rm p - 6=0\end{cases}$

$\rm :\longmapsto p = 6, -2$

★ So, the values of p are 6 and -2.

$\texttt{\textsf{\large{\underline{Learn More}:}}}$

The discriminant of an equation tells us about the nature of roots.

Standard form of a quadratic equation is:

$\rm :\longmapsto ax^{2}+bx+c=0$

Discriminant is calculated by using the formula:

$\rm :\longmapsto Discriminant=b^{2}-4ac$

1. When D > 0: Roots are real and distinct.

2. When D = 0: Roots are real and equal.

3. When D < 0: Roots are imaginary.