⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆ GIVEN⠀ POLYNOMIAL – 7x² – 18x + 11 : ⠀⠀⠀⠀ [tex]:\implies\sf 7x^2 -18x + 11 = 0 \\\\\\\star \sf{By \:Using\:Sum-Product \:Pattern\::}\\\\ \:\implies\sf 7x^2 – 7x – 11x + 11= 0 \\\\\\\star\sf{Finding\:out\:Common\:Terms\::}\\\\\\:\implies\sf 7x(x – 1) -11(x – 1) = 0\\\\\\\star\sf{Now,\:Rewrite\:in\:Factored\:term\::}\\\\\\:\implies\sf (7x – 11)\; (x – 1) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{x\:\:= \; \; 1\:\: \:or\:\:\:\dfrac{11}{7}}}}}}\;\bigstar[/tex] Therefore, ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence, \:The\:roots \:are\:\bf{1 \:and \:\dfrac{11}{7}\: }}}}\\[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Reply
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆ GIVEN⠀ POLYNOMIAL – 7x² – 18x + 11 :
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[tex]:\implies\sf 7x^2 -18x + 11 = 0 \\\\\\\star \sf{By \:Using\:Sum-Product \:Pattern\::}\\\\ \:\implies\sf 7x^2 – 7x – 11x + 11= 0 \\\\\\\star\sf{Finding\:out\:Common\:Terms\::}\\\\\\:\implies\sf 7x(x – 1) -11(x – 1) = 0\\\\\\\star\sf{Now,\:Rewrite\:in\:Factored\:term\::}\\\\\\:\implies\sf (7x – 11)\; (x – 1) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{x\:\:= \; \; 1\:\: \:or\:\:\:\dfrac{11}{7}}}}}}\;\bigstar[/tex]
Therefore,
⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence, \:The\:roots \:are\:\bf{1 \:and \:\dfrac{11}{7}\: }}}}\\[/tex]
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Answer:
7 and 11 are the root of the quadratic equation