Question

.Find the value of the discriminant of the equation x2+ 10x-7=0.​

Answer 1

$\underline{\frak{\quad \purple{Given:-} \quad}}$

$\sf \qquad \bullet {x}^{2} + 10x - 7 = 0$

$\underline{\frak{\quad \purple{Find:-} \quad}}$

$\sf \qquad \bullet Discriminant$

$\underline{\frak{\quad \purple{Solution:-} \quad}}$

Here, f1st compare given eq. with ax² + bx + c = 0

So,

a = 1

b = 10

c = -7

Now, Using

$\huge{\underline{\boxed{\sf Discriminant = {b}^{2} - 4ac}}}$

$\sf where \small{\begin{cases} \sf a = 1 \\ \sf b = 10 \\ \sf c = - 7\end{cases}}$

$\red\bigstar$ Substituting these values:-

$\dashrightarrow\sf D = {b}^{2} - 4ac$

$\dashrightarrow\sf D = {(10)}^{2} - 4(1)( - 7)$

$\dashrightarrow\sf D =100 - 4( - 7)$

$\dashrightarrow\sf D =100 + 28$

$\dashrightarrow\sf D =128$

$\small{\underline{\boxed{\sf \therefore Discriminant \: of \: eq. \: x^2 + 10x -7=0 \: is \: 128}}}$

Answer 2

$\huge\bigstar \: \huge\mathrm { \underline{ \purple{given} }} \: \bigstar$

• Equation is x² + 10x - 7

$\huge\bigstar \: \huge\mathrm { \underline{ \purple{to \: find} }} \: \bigstar \:$

• Discriminant.

$\huge\bigstar \: \huge\mathrm { \underline{ \purple{solution} }} \: \bigstar \:$

➔ Discriminant = b² - 4ac

Where ,

• a coefficient of x²

• b coefficient of x

• c constant

▬▬▬▬▬▬▬

Here ,

• a = 1

• b = 10

• c = -7

➥ Putting values , we get

$\sf \: {discriminant = {b}^{2} - 4ac} \\ \ \\ \sf{discriminant = {10}^{2} - 4(1)( - 7) } \\ \\ \sf{discriminant = 100 + 28}$

$\therefore \: \bf{ \red{discriminant \: = 128}}$

More to know :-

• The quadratic equation discriminant is important because it tells us the number and type of solutions. This information is helpful because it serves as a double check when solving quadratic equations by any of the four methods (factoring, completing the square, using square roots, and using the quadratic formula).