If -5 x2- 8x - 3-5 - 0 is factorized into the form -5 x2- px - qx - 3-5 - 0- then what is the value of p2 - q2 -

Multiply √(5) with 3√(5), we get 15 Pairs of 15 are: 1×15 = 15, sum: 1+ 15 = 16; not possible. 5×3= 15, sum: 5+ 3 = 8; possible. So, our required pair is 5 an ...

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Byju's Answer

Standard XIII

Mathematics

Factor Theorem

If √5 x2+ 8x ...

Question

If $\sqrt{5} x^{2} + 8 x + 3 \sqrt{5} = 0$ is factorized into the form $\sqrt{5} x^{2} + p x + q x + 3 \sqrt{5} = 0$ , then what is the value of $p^{2} + q^{2}$ ?

$9$

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$34$

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$25$

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$16$

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Solution

The correct option is B
$34$

Multiply $\sqrt{5}$ with $3 \sqrt{5}$ , we get $15$

Pairs of $15$ are:
$1 \times 15 = 15$ , sum: $1 + 15 = 16$ ; not possible.
$5 \times 3 = 15$ , sum: $5 + 3 = 8$ ; possible.

So, our required pair is $5$ and $3$ .
Hence, $p^{2} + q^{2} = 5^{2} + 3^{2} = 34$

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Similar questions

Factorize:

$5 \sqrt{5} x^{2} + 20 x + 3 \sqrt{5}$

If $\sqrt{5} x^{2} + 8 x + 3 \sqrt{5} = 0$ is factorized into the form $\sqrt{5} x^{2} + p x + q x + 3 \sqrt{5} = 0$ , then what is the value of $p^{2} + q^{2}$ ?

Factorize $\sqrt{5} x^{2} + 8 x + 3 \sqrt{5} = 0$ into the form $\sqrt{5} x^{2} + p x + q x + 3 \sqrt{5} = 0$ . What is the value of $p^{2} + q^{2}$ ?

Factorize $\sqrt{5}$ $x^{2}$ + 8x + 3 $\sqrt{5}$ = 0 into the form $\sqrt{5}$ $x^{2}$ + px + qx +3 $\sqrt{5}$ = 0.Find the value of p and q.

Q. If

5 x^{2} - 3 x - 2 = 0

, then

x = 3, - \frac{2}{5}

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If √5x2+8x+3√5=0 is factorized into the form √5x2+px+qx+3√5=0, then what is the value of p2+q2 ?

The correct option is B 34 Multiply √5 with 3√5, we get 15 Pairs of 15 are: 1×15=15, sum: 1+15=16; not possible. 5×3=15, sum: 5+3=8; possible. So, our required pair is 5 and 3. Hence, p2+q2=52+32=34

If $\sqrt{5} x^{2} + 8 x + 3 \sqrt{5} = 0$ is factorized into the form $\sqrt{5} x^{2} + p x + q x + 3 \sqrt{5} = 0$ , then what is the value of $p^{2} + q^{2}$ ?

The correct option is B
$34$

Multiply $\sqrt{5}$ with $3 \sqrt{5}$ , we get $15$

Pairs of $15$ are:
$1 \times 15 = 15$ , sum: $1 + 15 = 16$ ; not possible.
$5 \times 3 = 15$ , sum: $5 + 3 = 8$ ; possible.

So, our required pair is $5$ and $3$ .
Hence, $p^{2} + q^{2} = 5^{2} + 3^{2} = 34$