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For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity p2–3p+2 =0 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> p = 1, 2...(i) p2 – 5p + 4 = 0 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> p = 1, 4...(ii) p – p2 = 0 <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> p = 0, 1...(iii) For (i), (ii) &amp; (iii) to hold simultaneously p = 1.

Number of values of 'p' for which the equation<img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0" width="326" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced separators=¨|¨»«mrow»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»§#8722;«/mo»«mn»3«/mn»«mi»p«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfenced»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#8722;«/mo»«mfenced separators=¨|¨»«mrow»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»§#8722;«/mo»«mn»5«/mn»«mi»p«/mi»«mo»+«/mo»«mn»4«/mn»«/mrow»«/mfenced»«mi»x«/mi»«mo»+«/mo»«mi»p«/mi»«mo»§#8722;«/mo»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»0«/mn»«/math»'/> possess more  than two roots ,is:

Solution for the question - number of values of 'p' for which the equation(p^(2)-3p+2)x^(2)-(p^(2)-5p+4)x+p-p^(2)=0 possessmore than two roots,is: none