Question

5. 'p(x^(2) x) q=0' is a root of the quadratic equation 'dots..' . For '2x^(2) px-15=0' value ofq, the equation '-3' has equal roots.​

Answer 1

Answer:

The two main forms of carbohydrates are sugars (such as fructose, glucose, and lactose) and starches, which are found in foods such as starchy vegetables, grains, rice, breads, and cereals. The body breaks down (or converts) most carbohydrates into the sugar glucose, which is absorbed into the bloodstream.

Step-by-step explanation:

Answer 2

$\Large{\textbf{\underline{\underline\pink{According\:to\:the\:Question}}}}$

Root is -5

Root is -52x² + px - 15 = 0 ...(1)

$\textbf{\underline{Equal\;Roots :- }}$

p(x² + x ) + k = 0 (2)

${\boxed{\sf\red{Substitute\;value\;of\;x\;in\;(1)}}}$

⇝ 2x² + px - 15 = 0

⇝ 2(-5)² + p(-5) - 15 = 0

⇝ 2 × 25 - 5p - 15 = 0

⇝ 50 - 5p - 15 = 0

⇝ 35 - 5p = 0

⇝ 5p = 35

$✯\tt{\rightarrow p=\dfrac{35}{5}}✯$

${\boxed{\sf\:{Substitute\;value\;of\;p\;in\;(2)}}}$

• ⇝ p(x² + x ) + k = 0

• ⇝ 7(x² + x ) + k = 0

• ⇝ 7x² + 7x + k = 0

✯Here we have, ✯

${\boxed{\sf\:{a = 7\;,\;b = 7\;and\;c = k}}}$

D = b² - 4ac

$\textbf{\underline\red{Quadratic\;equation\;has\;equal\; roots}}$

• ⇝ D = 0

• ⇝ b² - 4ac = 0

• ⇝ 7² - 4(7)(k) = 0

• ⇝ 49 - 28k = 0

• ⇝ 49 = 28k

$\sf{\rightarrow k=\dfrac{49}{28}}$

$\sf{\rightarrow k=\dfrac{7}{4}}$

$\sf{\underline{Therefore}}$

$\rm{\rightarrow k=\dfrac{7}{4}}$

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