Question

The discriminant of the quadratic equation 3x²+4x–2=0 is ____.

Answer 1

$\huge{\underbrace{\sf{\red{Required\:Answer:}}}}$

• We know that the standard form of quadratic equation is

$\large{\boxed{\sf{\pink{ax^{2}+by+c}}}}$

• If we compare the given equation with the standard form.We get,

$\displaystyle{\sf{ a = 3,b=4 and c = -2}}$

★$\large{\boxed{\sf{\orange{Discriminant(D) = b^{2} - 4ac}}}}$★

Substituting the values, we get

:$\implies{\sf{ D = (4)^{2} - 4\times 3\times (-2)}}$

:$\implies{\sf{ D = 16 - (-24)}}$

:$\implies{\sf{ D = 16 + 24}}$

:$\large\implies{\boxed{\sf{\purple{ D = 40}}}}$

Hence, the discrimimant of the equation 3x²+4x–2=0 is 40.

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What is a quadratic equation?

A quadratic equation ( derived from the Latin quadratus for "square") is any equation that can be re-arranged in standard form of ax² + by + c. where x and y represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0 and b ≠0.

Examples -

• 4x² + 9y + 7
• 5a² + 2b + 3

_____________________

Answer 2

$\boxed{\mathfrak\purple{Discriminant \: of \: quadratic \: equation = 40}}$

Given:

• Quadratic equation = 3x² + 4x - 2 = 0.

To Find:

• Value of Discriminant (∆) = ?

Solution:

Comparing 3x² + 4x - 2 = 0 with ax² + bx + c = 0.

Here,

• $\mathfrak{a = 3}$

• $\mathfrak{b = 4}$

• $\mathfrak{c = - 2}$

We know that,

$\star \: \boxed{\mathfrak\green{\delta = {b}^{2} - 4ac}}$

Substituting values,

$:\implies\mathfrak{ {4}^{2} - 4 \times ( - 3) \times ( - 2)} \\ \\ \\ \\ \\ :\implies\mathfrak{16 - 12 \times ( - 2)} \\ \\ \\ \\ \\ :\implies\mathfrak{16 + 24} \\ \\ \\ \\ \mathfrak\star \: \underbrace\red{\delta \: = \: 40} \: \star$

Hence,

• Value of Discriminant is 40.