Question

What is the nature of the roots of the quadratic equation 9 x2+25 = 3 0x ? *​

Answer 1

Appropriate Question :-

What is the nature of the roots of the quadratic equation 9x² + 25 = 30x.

Answer :-

• roots of the equation are real and equal.

Step by step explanation :-

Given Quadratic Equation : 9x² + 25 = 30x

First know the general form of quadratic equation,

➳ ax² + bx + c = 0

Writing the given quadratic equation in the general form.

➳ 9x² - 30x + 25 = 0

Concept :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac.

Now,

Comparing the given quadratic equation with the general form.

We get,

➢ a = 9

➢ b = -30

➢ c = 25

According to the concept,

Discriminant, D = b² - 4ac.

Substituting the values,

$\rm:\implies{D = ( - 30) {}^{2} - 4(9)(25) } \\ \\ \rm:\implies{D =900 - 4(225) } \: \: \: \: \: \: \: \: \: \\ \\ \rm:\implies{D = 900 - 900 = \boxed{0}} \: \: \:$

According to the concept,

If Discriminant, D = 0, then roots of the equation are real and equal.

Our discriminant is 0.

Hence,

Nature of roots : roots of the equation are real and equal.

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Answer 2

Step-by-step explanation:

Appropriate Question :-

What is the nature of the roots of the quadratic equation 9x² + 25 = 30x.

Answer :-

roots of the equation are real and equal.

Step by step explanation :-

Given Quadratic Equation : 9x² + 25 = 30x

First know the general form of quadratic equation,

➳ ax² + bx + c = 0

Writing the given quadratic equation in the general form.

➳ 9x² - 30x + 25 = 0

Concept :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac.

Now,

Comparing the given quadratic equation with the general form.

We get,

➢ a = 9

➢ b = -30

➢ c = 25

According to the concept,

Discriminant, D = b² - 4ac.

Substituting the values,

\begin{gathered}\rm:\implies{D = ( - 30) {}^{2} - 4(9)(25) } \\ \\ \rm:\implies{D =900 - 4(225) } \: \: \: \: \: \: \: \: \: \\ \\ \rm:\implies{D = 900 - 900 = \boxed{0}} \: \: \: \end{gathered}:⟹D=(−30)2−4(9)(25):⟹D=900−4(225):⟹D=900−900=0

According to the concept,

If Discriminant, D = 0, then roots of the equation are real and equal.

Our discriminant is 0.

Hence,

Nature of roots : roots of the equation are real and equal.

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