Question

 If the sum of the roots of the quadratic equation 3x² - kx + 9 = 0 is 5, then the value of 'k' is _______​

Answer 1

Answer

• The value of k = 15.

Given

• The sum of zeros of the quadratic polynomial 3x² - kx + 9 = 5.

To Do

• To find the value of k.

Step By Step Explanation

On comparing :

Let's compare 3x² - kx + 9 with ax² + bx + c.

Here, a = 3, b = -k and c = 9.

We know that :

$\bigstar \: \: \: \: \underline{\boxed{ \tt{ \red{\alpha + \beta = \cfrac{ - b}{a}}}}}$

By substituting the values :

Let's substitute the values in the above formula to find the value of k.

$\longmapsto \sf \alpha + \beta = \cfrac{ - b}{a} \\ \\\longmapsto \sf 5 = \cfrac{ - ( - k)}{3} \\ \\\longmapsto \sf 5 = \cfrac{k}{3} \\ \\\longmapsto \sf 5 \times 3 = k \\ \\\longmapsto \underline{\boxed{ \bold{ \green{15 = k}}}} \: \: \: \: \dag$

Therefore, the value of k = 15.

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More to Know

• Polynomial - An algebraic expressions in which the variable involved having non negative integral power is known as polynomial.

• Quadratic polynomial - A polynomial of degree 2 is known as quadratic polynomial.

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Answer 2

Answer:

15

Step-by-step explanation:

$\large{\underline{\underline{\mathfrak{Given:-}}}}$

the sum of the roots of the quadratic equation 3x² - kx + 9 = 0 is 5

$\large{\underline{\underline{\mathfrak{To\:Find:-}}}}$

• Value of k= ?

$\large{\underline{\underline{\mathfrak{Concepts:-}}}}$

• Sum of the roots = -b/a

$\large{\underline{\underline{\mathfrak{Solution:-}}}}$

In the quadratic equation 3x² - kx + 9 = 0, sum of the roots is 5

We know that,

Sum of the roots = -b/a

So,

-b/a=5

here, b is -k and a is 3

put the values of b and a :-

-(-k)/3=5

k=5×3

k=15

$\large{\underline{\underline{\mathfrak{Useful\: Formulae:-}}}}$

• Product of zeroes= c/a
• Sum of roots of cubic polynomial= -b/a
• product of roots of cubic polynomial= -d/a