Question

Find the value of p for which one root of the quadratic equation px2-14x+8=0 is 6 times the other.

Chapter: Linear equation in two Variables
Class : 10th​

Answer 1

see attachment.

$\large\boxed{\textsf{\textbf{\orange{ANSWER\::-}}}}$

Given: The area of a trapezium is 34 cm² & it's Height is 4 cm. also, one of the // side of the trapezium is 10 cm.

Need to find: The Length of other // side?

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❍ Let' say, that the other // side of the trapezium be x cm respectively.

As we know that,

⭒To calculate Area of Trapezium Formula Given by :

$\quad\star\:\;\underline{\boxed{ \bf{\frak{Area_{\:(trapezium)} = \dfrac{1}{2} \times \Bigg(a + b \Bigg) \times h}}}}$

where:

a & b are the sides of the trapezium.

h is the height of trapezium.

& Area is given.

⠀

⠀$\underline{\bf{\dag} \:\mathfrak{Putting\;Values\;in\; formula\: :}}$⠀⠀⠀⠀

$\:\;\;:\implies\sf 34 = \dfrac{1}{\cancel{\;2}} \times \Bigg(10 + x\Bigg) \times \cancel{\;4} \\\\\\:\implies\sf 34 = \Bigg(10 + x\Bigg) \times 2\\\\\\:\implies\sf 34 = 20 + 2x\\\\\\:\implies\sf 34 - 20 = 2x\\\\\\:\implies\sf 14 = 2x\\\\\\:\implies\sf x = \cancel\dfrac{14}{2}\\\\\\:\implies\underline{\boxed{\pmb{\frak{x = 7 ~cm}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence, the length of other parallel side is \textbf{7 cm}.}}}$

Answer 2

The poem "I'm Looking Over a Four-Leaf Clover" by Mort Dixon and Harry M. Woods is a popular song that has become a symbol of good luck. Each leaf of the clover has its own significance, and the poem encourages us to find a four-leaf clover for good luck.

According to the Encyclopedia Britannica (Print), the four-leaf clover is a rare variation of the common three-leaf clover, which is a symbol of Ireland. Each leaf of the clover represents something different: the first is for faith, the second is for hope, the third is for love, and the fourth is for luck.

The Oxford English Dictionary (Print) defines a four-leaf clover as "a clover with four leaves instead of three, traditionally considered to bring good luck."

In their book "The Folklore of Plants" (Print), T. F. Thiselton-Dyer and Margaret Grieve write that the four-leaf clover has been considered a lucky charm since ancient times. They also note that finding one is said to be difficult because there is only one four-leaf clover for every 10,000 three-leaf clovers.

As for what the poet requires us to do, the poem encourages us to "look over" a four-leaf clover in order to find good luck. The central idea of the poem is that finding a four-leaf clover will bring good fortune.

Four rhyming words from the poem are "over," "clover," "fields," and "yields."