Question

Use the discriminant to determine how many real number solutions exist for the quadratic equation −3x2 + 4x − 13 = 0.

Answer 1

Hey there,

Use the discriminant to determine how many real number solutions exist for the quadratic equation:

-3x² + 4x - 14 = 0

∆ = b² - 4ac

∆ = 4² - 4*(-3)*(-14)

∆ = 16 - (-12)*(-14)

∆ = 16 - 168

∆ = -152

∆ = -152 < 0 ; There is no real number solution for the quadratic equation

S= { ø }

✅✅;-)

Answer 2

• No real solution

Explanation:

In the question we have given an equation that is -3x² + 4x - 13 = 0 and we are asked to determine how may real number of solutions exist for given quadratic equations .

We Know That ,

b² - 4ac determines whether the Quadratic Equation ax² + bx + c = 0 has real roots or not , b² - 4ac is called discriminant of this quadratic equations .

So , a quadratic equation ax² + bx + c = 0 has

(i) Two distinct real roots , if b² - 4ac > 0 ,

(ii) Two equal roots , if b² - 4ac = 0 ,

(iii) No real roots , if b² - 4ac < 0 .

In given equation −3x² + 4x − 13 = 0 ,

• a = -3

• b = 4

• c = -13

Solution : -

`\longrightarrow \: \pink{ \boxed{ D = b {}^(2) - 4ac}} \longleftarrow`

Substituting values :

`\longmapsto \: D = (4) {}^(2) - 4( - 3)( - 13)`

Calculating further :

`\longmapsto \: D = 16 - 4(39)`

`\longmapsto \: D = 16 -156`

`\longmapsto \: \boxed{\bold{ D = - 140}}`

Here discriminant is less than 0 ( D = -140 < 0 ) .

• Henceforth , there is no real solution exist for the given Quadratic Equation.

#Keep Learning