Question

find the value of discriminant
${2x}^{2} - 5x + 10 = 0$
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Answer 1

Given :

• 2x²-5x+10

To find :

• Discriminant of the given equation

Formula used :

• D = b²-4ac

where :-

• D = discriminant
• b = coefficient of x
• a = coefficient of x²
• c = constant term

Solution :

=> 2x²-5x+10

Here ,

• a = 2
• b = -5
• c = 10

Now we will find discriminant :-

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

$\sf \implies D = {( - 5)}^{2} -(4 \times 2 \times 10)$

$\sf \implies D = {( - 1)}^{2} {( 5)}^{2} -(4 \times 2 \times 10)$

5² = 25

(-1)²= 1

$\sf \implies D = 25-80$

$\sf \implies D =-55$

Answer :

Discriminant of given quadratic equation 2x²-5x+10 is = -55

Answer 2

Answer:

Given :-

• 2x² - 5x + 10 = 0

To Find :-

• Discriminant (D)

Solution :-

Given equation :

$\mapsto$ 2x² - 5x + 10 = 0

➣ a = 2, b = - 5, c = 10

Since, the two roots are real and equal.

➠ Discriminate = b² - 4ac

⇒D = (- 5)² - 4.2.10

⇒D = (- 5)(- 5) - 80

⇒ D = 25 - 80

➥ D = - 55

∴ The Discriminant of 2x² - 5x + 10 = 0 is $\boxed{\bold{\large{-\: 55}}}$

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❖ Extra Information ❖

✦ The two roots of the quadratic equation ax² + bx + c = 0,

❶ Real and equal = b² - 4ac = 0

❷ Real and unequal = b² - 4ac > 0

❸ No real root = b² - 4ac < 0

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