Question

Find the value of q so that the equation 2x²-3px+ 5q = 0 has one root which is twice the other.
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Answer 1

$\large\bf\underline \orange{Given:-}$

• p(x) = 2x² - 3px + 5q = 0

$\large\bf\underline \orange{To \: find:-}$

Value of q

$\huge\bf\underline \red{\dag\:\:\:Solution:-}$

Standard form of quadratic equation :-

• ax² + bx + c = 0

Given quadratic equation is

p(x) = 2x² - 3px + 5q = 0

where,

• a = 2
• b = - 3p
• c = 5q

Let α and β are the roots of the given polynomial.

It is given that one root is twice the other,

Then,

⠀⠀⠀⠀⠀➝ β = 2α

we know that,

sum of zeroes = - b/a

• α + β = - b/a

⠀⠀⠀⠀⠀➝ α + 2α = -(-3p)/2

⠀⠀⠀⠀⠀➝ 3α = 3p/2

⠀⠀⠀⠀⠀➝ α = 3p/6

⠀⠀⠀⠀⠀➝ α = p/2 ..........(i)

Now,

Product of zeroes = c/a

• αβ = c/a

⠀⠀⠀⠀⠀➝ α ×2α = 5q/2

⠀⠀⠀⠀⠀➝ 2α² = 5q/2

⠀⠀⠀⠀⠀➝ 2α² ×2 = 5q

⠀⠀⠀⠀⠀➝ 4α² = 5q ...........(ii)

putting value of α from (i) in (ii) ,we get,

⠀⠀⠀⠀⠀➝ 4(p/2)² = 5q

⠀⠀⠀⠀⠀➝ 4 × p²/4 = 5q

⠀⠀⠀⠀⠀➝ p² = 5q

⠀⠀⠀⠀⠀➝ p² -5q = 0

⠀⠀⠀⠀⠀➝ q = -p²/-5

⠀⠀⠀⠀⠀➝ q = p² /5

⠀⠀⠀⠀⠀➝ q = p² /5

Hence,

value of q is p²/5.

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Answer 2

Answer:

thanks niharika I asked u because in our school they told us to write the notes so I had some doobts and once again thank u dear

and u send another lesson in my any question

and also report my this answer