Question

11x²-54x+63 splitting the middle term

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=3\:and\:\frac{21}{11}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {11x}^{2} - 5x + 63 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: x = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {11x}^{2} - 54x + 63 = 0 \\ \\ \tt: \implies {11x}^{2} - 33x - 21x + 63 = 0 \\ \\ \tt: \implies 11x(x - 3) - 21(x - 3) = 0 \\ \\ \tt: \implies (11x - 21)(x - 3) = 0 \\ \\ \green{\tt: \implies x = \frac{21}{11} \: and \: 3} \\ \\ \bold{Alternate \: method : } \\ \\ \tt \circ \: a = 11 \: \: \: \: \: \: b = - 54 \: \: \: \: \: \: c = 63\\ \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies \frac{ - ( - 54) \pm \sqrt{ {( - 54)}^{2} - 4 \times 11 \times 63} }{2 \times 11} \\ \\ \tt: \implies x = \frac{54 \pm \sqrt{2916 - 2772} }{22} \\ \\ \tt: \implies x = \frac{54 \pm \sqrt{144} }{22} \\ \\ \tt: \implies x = \frac{54 \pm12}{22} \\ \\ \tt: \implies x = \frac{54 + + 12}{22} \: and \: \frac{54 - 12}{22} \\ \\ \tt: \implies x = \frac{66}{22} \: and \: \frac{42}{22} \\ \\ \green{\tt: \implies x = 3 \: and \: \frac{21}{11} }$

Answer 2

Aɴꜱᴡᴇʀ

➤ Roots of the equation are, $\large\bf\frac{21}{11}\: and \: 3$

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Gɪᴠᴇɴ

➠ To use splitting method on 11x² - 54x + 63

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ᴛᴏ ꜰɪɴᴅ

✴ The roots of the given equation?

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Sᴛᴇᴘꜱ

✭ In this method we have to split the middle term (here 54x) in a defined manner (How do do that has been given as an attachment)

✭ Here the x² term has 11 as a cofficient so when splitting the middle term we have to multiply the coefficient of the x² term with the constant [Here 11 × (-63) = 693]

$\large \tt \dashrightarrow{}11 {x}^{2} -33x - 21x + 63x = 0 \\ \\ \large \tt \dashrightarrow11x(x - 3) - 21(x - 3) = 0 \\ \\ \large \tt \dashrightarrow \orange{(11x - 21)}{ \green{(x - 3) }}= 0$

☞ So now let's equate each one with 0 to find the roots of the given equation,

$\large \tt \leadsto11x - 21 = 0 \\ \\ \large \tt \pink{\leadsto{}x = \frac{21}{11} }$

And,

$\large \tt \longmapsto{}x - 3 = 0 \\ \\ \large \tt \pink{ \longmapsto{}x = 3}$

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